A coat of arms is a symbol, usually painted on an escutcheon (a shield), that represents a country, institution, Royal Personage or member of the noble class. Some coats of arms are painted on an oval or lozenge instead of a shield, because they belong to a noble woman or a member of the clergy, and they were forbidden to fight in the military in medieval society, so they would not use a shield.
Some people confuse the terms coat of arms and crest, thinking that a coat of arms is a "family crest", but in actual fact, a crest is something placed on top of a helmet displayed above the coat of arms. Many people in England passed their crest down the family line, but each person in the family had a different shield, leading to the term "family crest", but in Germany and Scandinavia, the shield would often be passed down the generations without changes while each member of the family had a different crest.
A display of heraldry including other parts around the coat of arms or shield is called an achievement of arms. This includes the escutcheon or shield displaying the coat of arms, a helm (helmet) which is usually wrapped with a torse and draped with a mantle and sometimes surmounted by a coronet of rank (or royal crown for the King or kingdom, imperial crown for the Emperor, or papal tiara for the Pope) and crest, and the shield may or may not be held up by a pair of animals called supporters. The whole thing is sometimes placed upon a sconce or compartment, and sometimes a banner is also displayed, showing a motto or battle cry. Many of these elements began to appear only at the end of the Middle Ages, and each was symbolic of social or governmental status. A wealthy merchant without noble titles might have a coat of arms (and probably a helmet, torse, mantle and crest) but would not have a coronet of rank, supporters, compartment or motto.