An achievement of arms is what you usually see when people in the mundane world try to sell you merchandise with 'your family coat of arms' on it. It's a display of arms with decorative elements which are meaningful to the arms bearer. As most SCAdians know, a coat of arms does NOT belong to anyone with the same family name and only the eldest member of the family is entitled to it, if the family does have arms. The rules for succession are not unlike the rules for who gets to wear the crown of England. In the SCA, each individual can register their own arms.
The purpose of this article is to explain the parts of an achievement to encourage others to design and use their own achievements to increase the heraldic display at events.
"Fourteen Kingdoms regulate by law or custom the components of Arms. Those fourteen kingdoms are: An Tir, Ansteorra, Artemesia, Atenveldt, Atlantia, Caid, Calontir, Ealdormere, Gleann Abhann, Meridies, Middle, Outlands, Trimaris, West. The remaining five do not: AEthelmearc, Drachenwald, East, Lochac, Northshield" The paper includes an easy-to-read chart of what is restricted where. This document was recently discussed on the SCA Heraldry Chat Facebook page and there have been a few minor changes since the article was written.
AEthelmearc does NOT have any laws or restrictions regarding what you can include in your achievement, however courtesy demands that you only include regalia your persona is entitled to. The practical list of restricted regalia may be found at http://tasha.gallowglass.org/sca/sumptuary.html. All parts of an achievement are optional, and everything except the shield (your registered device) may be changed at will.
SHIELD -- This is your registered heraldic device. This is the only part that cannot be changed at will. What's the difference between 'heraldic device' and 'arms'? Virtually nothing. The latter says that you have been awarded arms but the terms are used nearly interchangably.
SUPPORTERS -- The figures to either side that hold up or 'support' the shield. In modern England, the use of supporters is only allowed to the peerage.
“In England the right to bear supporters is confined to those to whom they have been granted or recorded, but such grant is very rigidly confined to peers, to Knights of the Garter, Thistle, and St. Patrick, and to Knights Grand Cross and Knights Grand Commanders (as the case may be) of other Orders. [...] Baronets of England, Ireland, Great Britain, and the United Kingdom as such are not entitled to claim grants of supporters...” 
Some kingdoms allow one supporter for anyone having a grant of arms and two supporters for anyone with a peerage. Other kingdoms only allow supporters to people with an augmentation of arms. AEthelmearc has no rules regarding supporters.
The modern arms of England have a lion and a unicorn representing England and Scotland. Historically, other animal supporters have included Boars, Antelopes, Eagles and Dragons depending upon who was on the throne at the time.  I'm utterly convinced that this is the origin of football mascots, but I can't prove it. I can picture medieval knights in a tournament having their junior-most squires holding their banner while dressed as their supporters. From there, it's just a small jump to a guy in an animal costume at a football rally.
THE COMPARTMENT -- Simply the base that supporters stand on. It's usually a green hill, 'a mount vert', in heraldic parlanance. It's optional and supporters can stand on the scrollwork of the motto if you don't want to have a compartment. In Real World heraldry, members of an order of knighthood often place a symbol of the order in their compartment. You can do this as well, but too many symbols may make the achievement look cluttered, simple is best.
SCROLL, RIBBON AND MOTTO -- Most mottos scroll along the bottom around the achievement, some scroll along the top around the mantling. A few have both. The motto can be in any language you want. If you want something in a language you're not fluent in, ask a herald for help, we may be able to steer you towards someone who is fluent in the language you want. After all, you want your motto to say "Get a Life", not "Take a Life"! If the armiger is a member of an order, the order's motto can be inscribed on a ribbon which circumscribes the shield. England has "Dieu et mon droit" ("God and my right") on a scroll in the compartment and the Order of the Garter's motto, "Honi soit qui mal y pense" ("Evil to him who thinks evil") on a garter or belt encircling the shield. 
HELMET -- The helmet sits upon top of the shield. Traditionally, clergical arms and women who display their arms on lozenges would not have a helm. Most SCAdians would use a helmet that was appropriate to their persona's time and place. In modern heraldry, the helm is used to indicate the armiger's rank. This is NOT a period practice.
“...at the end of the sixteenth and the beginning of the seventeenth centuries, when the helmet was being fast relegated to ceremonial usage and pictorial emblazonment, ingenious heralds began to evolve the system by which rank and degree were indicated by the helmet.” However, for those who want to;
"as one of the fundamental laws of the achievement, that the helmet by its shape and position was indicative of rank ; and we early learnt by rote that the esquire’s helmet was of steel, and was placed in profile, with the visor closed : that the helmet of the knight and baronet was to be open and affronté ; that the helmet of the peer must be of silver, guarded by grilles and placed in profile ; and that the royal helmet was of gold, with grilles, and affronté. ... These regulations, like some other adjuncts of heraldic art, are comparatively speaking of modern origin. Heraldry in its earlier and better days knew them not, and they came into vogue about the Stuart times, when heraldic art was distinctly on the wane." 
TORSE AND MANTLING -- The torse is a twisted ring of fabric which holds the mantling
in place on a knight's helmet. The mantling itself was fabric which was used to keep
the hot sun off a crusader's metal helmet and most likely evolved around the time of
the First Crusade. 
"Generally, mantling is blazoned 'mantled x, doubled (lined) y'"
The tinctures x and y should be strongly contrasting, usually a color and a metal,
however the arms of the United Kingdom are mantled Or and ermine.
I have never seen a torse of different tinctures than the mantle, but I don't know
of any reason why it couldn't be done.
CROWN / CORONET -- A crown can be placed atop a torse or as a replacement for it. A coronet can be placed in the same position as a crown or around the neck of the helm or a supporter. For reasons of courtesy, you should only have a crown or coronet on your achievement if your persona is allowed one. An SCA ducal coronet has strawberry leaves on it. A county coronet has an embattled top edge. A baronial coronet has six pearls on it. If you are entitled to more than one type of tin hat, you could have both of them in your achievement, if you wished. The arms of the United Kingdom have crowns on the helm, on the head of the lion supporter, on the head of the lion crest and a coronet around the neck of the unicorn supporter 
CREST -- Primarily used as a decoration in tournament, the crest goes atop the helm. It is possible for a heraldic crest to be something that couldn't be used in real life. The crest of Sir Francis Drake granted in 1581 consisted of a disembodied hand issuing from clouds and leading a ship around the globe representing God's guidance  
RESERVED REGALIA -- As I said above, as a matter of courtesy, you should have reserved symbols or regalia on your achievement only if your persona is entitled to it. A pelican would be entitled to use a pelican as a supporter or their crest, or replacing the crown / torse with a cap of maintenance (a red 'robin hood' cap trimmed with white that has little red drops of blood on it) A knight could his a white belt or a gold chain as a ribbon surrounding the shield. A Master of Arms would have a white baldric instead of a white belt. In a similar fashion, a lady of the rose could have a wreath of roses or a laurel could have a laurel wreath.
My own achievement: "Barry wavy vert and argent, a unicorn's head sable, armed (teeth and horn), orbed (eyed), and crined (maned), a chief wavy Or; for a Crest, atop a helm to dexter argent, a raven proper; a torse and mantle argent and doubled vert; for Supporters, two unicorns sable armed, orbed and crined Or, on a mount vert; Motto 'Post Mortum Concedo' (After Death, I will yield) argent lettered sable."
The supporters on my achievement are black unicorns to match my device. My steel-colored helm faces to the side as a citizen. My crest is a raven as a tribute to my wife (Cigfran is the Welsh word for 'raven')
"This uncredited leather project shows the heraldic achievement of the Rhydderich Hael. The original artwork was designed by Master Dagonell. Master Dagonell reports: 'The shield is the arms of the Rhydderich Hael. The helm faces to the side instead of forward because only royalty face forward. (Out of period practice, but still widely used) The mantle and torse are supposed to be green and yellow with black gunstones to represent the Hael livery colors and Haelstones (Hael service award). The crest is a ram skull taken from the arms of the first baroness Morgan Elandris. The supporters are a blue tyger to represent that we started in the East and a heron in it's vigilance to represent The Shire of Heronter which spun off from us. The compartment (ground) contains a Catherine's wheel and a fountain to represent Winter's Edge and Beau Fleuve (cantons). The scroll is supposed to contain the motto, Non Sine Labora "Nothing is without Effort"'. Who decided to use this for a leather project or why is unknown. Sadly the leather is worn with time and the project was never finished." 
This is an achievement I designed for The AEstel back when Lord Gareth the Eccentric was chronicler. The supporters are blue tyger engorged of a coronet as a reminder that we were once part of the East, and a golden alce to represent the Golden Alce, the third original order of merit. Technically, the tyger should have a crown, but I liked the aestetics of the coronet around his neck better. :) Instead of a ribbon encircling the shield, I crossed a sword and a marshal's baton behind it to represent the Pennsic War which takes place in our kingdom. The helm faces forward as this is a royal achievement, and wears a copy of the crown that was being used at the time the achievement was drawn. The crest is a sea-lion, a reference to the Great Lakes. One of the names submitted for the original principality was 'The Principality of the Lakes'. The compartment contains a sycamore leaf and a keystone and to represent two of AEthelmearc's original orders of the Keystone and Sycamore.
This is a photo of the scroll carrier used in royal court to carry the scrolls. Photo by Master Kameshima Zentarou Umakai, Silver Buccle Herald Emeritus and used with permission. The artist is unknown. The supporters are golden alces, there is no compartment or motto on the scroll. The crown faces to dexter, but is crowned.
This is a photo of the T-shirts that were sold at the Coronation of Yngvar and Caryl. It consists only of shield, helm, torse and mantling. The helm is sideways, but is crowned. Photo by Mistress Hilderun Hugelmann, and used with permission. The artist is unknown.
This is the achievement from the Midrealm's Great Book of scroll wordings found at: http://www.midrealm.org/mkgb/GreatBookContents.html. The mantling is ermine and gules, rather than argent and gules, the helm faces to the side, but is crowned. The supporters and crest are dragons to match the midrealm shield. The artist is unknown.
This is the achievement from Ealdormere's History Blog found at: http://ealdormerehistory.blogspot.com/2013/10/rise.html, designed by His Excellency Liadin. The mantling is gules and argent to match their arms, the helm is to the side but crowned, the supporters are collared wild dogs, the crest is a wild dog passant with a trillium flag to match their arms, the compartment is a field of trillium blossums, the motto is "We Wear the Scarlet Proudly". I do not know the symbolism of the wild dogs.
The official blazon of the Royal Arms is:
"Quarterly, first and fourth Gules three lions passant gardant in pale Or armed and langued Azure (for England), second quarter Or a lion rampant within a double tressure flory-counter-flory Gules (for Scotland), third quarter Azure a harp Or stringed Argent (for Ireland), the whole surrounded by the Garter; for a Crest, upon the Royal helm the imperial crown Proper, thereon a lion statant gardant Or imperially crowned Proper; Mantling Or and ermine; for Supporters, dexter a lion rampant gardant Or crowned as the Crest, sinister a unicorn Argent armed, crined and unguled Proper, gorged with a coronet Or composed of crosses patée and fleurs de lis a chain affixed thereto passing between the forelegs and reflexed over the back also Or. Motto 'Dieu et mon Droit' in the compartment below the shield, with the Union rose, shamrock and thistle engrafted on the same stem." 
Serious heraldry squee!! On October 2nd, 2017, former astronaut Julie Payette was installed as the 29th Governor General of Canada. Her arms were designed by the Canadian Heraldic Authority under the approval of Claire Boudreau, chief herald of Canada. For full details, check the links in the footnotes, I'm summarizing here for simplicity.   BTW, the Ridley Hall mentioned in the articles, is the official residence of the Governor General. It's the Canadian version of 'The White House said...'
ARMS -- "Per pale azure and sable, overall a sinister wing, in dexter chief a royal crown, all argent." -- the blazon for her arms, I haven't seen an official citation, but I'm a herald. :) "A symbol of exploration and liberty, an open wing embodies our desire to reach higher and expand our horizons. As with birds protecting their young, the wing also conveys the strength and safety of family ties. Moreover, it represents Ms. Payette’s career as an aviator and astronaut. The Royal Crown symbolizes the viceregal office and service to all Canadians." 
RIBBON -- The red ribbon encircling her arms is labelled in gold. DESIDERANTES MELIOREM PARIAM, which translates to "desiring a better country," the official motto of the Order of Canada.
SUPPORTERS -- "Making a nod to the cat perched atop “La fusée de Julie,” the emblem created by Quebec artist Gérard Dansereau of Ms. Payette’s first space mission, STS-96, the two lynx, proud and strong, represent us, the people of Canada. An elusive feline, the Canada lynx is remarkably well adapted to northern territories, particularly because of its enormous paws that allow it to move easily through the snow. The stars around their necks represent the spark of passion in each of us, inspiring us to dare to dream. They also evoke space travel and the work environment of astronauts. The laurel leaves – laurier in French – depicted alongside the stars represent Laurier, Ms. Payette’s son." 
HELMET, TORSE, MANTLING -- Her helmet is an astronaut's helmet representing her former career as an astronaut. Squee!! The torse and mantling is azure, sable and argent, the tinctures of her arms.
CREST -- "At the top, a musical stave, a melody, symbolizes the creativity, sensitivity and remarkable virtuosity of human beings. The first notes of the second movement of Alessandro Marcello’s 'Oboe Concerto in D Minor' evoke Ms. Payette’s lifelong interest in singing and classical music, particularly from the Baroque period. 
COMPARTMENT -- "Represented here as seen from space, without borders and surrounded by a thin layer of atmosphere, our planet resembles a blue marble on a backdrop of darkness. It remains the only place where humans can live. The mathematical symbol for the sum, S (sigma), placed in its centre, illustrates the power of facts and science, and reminds us that we share the Earth and a responsibility to care for it." 
"The coat of arms is supported by the planet Earth, without borders, the way Payette would have seen it from space. Payette is a Companion of the Order of Canada (of which she is now Chancellor) and a Knight of the National Order of Quebec, and those two honours are depicted over the Earth." 
MOTTO -- "Translated from Latin 'Per Aspera Ad Astra' means 'Through hardship to the stars.' It's a motto used by Payette and her fellow astronauts to symbolize that there is hope in every situation, we just need to look for it."