A coat of arms is a shield or lozenge (usually displayed on the forum signature), designed for that person by the College of Heralds. It comes in three shapes: shield for men, and for women who prefer the more military shape, ornate for priests, and lozenge for women who prefer to use that instead of the shield. (The lozenge follows real-life heraldic tradition https://en.wikipedia.org/wiki/Heraldry#Shield, which was based on the reasoning that a shield was inappropriate for a woman's arms as she would not use a sword and shield in real life. This is, of course, far from the case in RK).
All persons on RK, regardless of level, nobility, or "age", are entitled to apply for a coat of arms, and usually include something personal to themselves, such as a real-life family coat of arms, favourite animal or colour etc.
As that person rises in noble rank, a coronet is added to the arms to show that rank. Commoner Heralds also have a coronet. The arms may have other arms added (marshalled) to show a link to a family, the town of residence, a marriage or the arms of their lands, if they are a noble.