In
heraldry, a crest is a small emblem perched on top of the coat of arms. In origin it is a kind of nodding dog or furry dice affixed to the
knight's
helmets, though they usually went for things like the top half of a lion as their decorative bit.
Often the term 'crest' is erroneously used for the whole shield or coat of arms, or the design on it. This is bad heraldry and should not be said.
A coat of arms always has a shield, with some design on it. It may have other things around the shield, or you might find the shield displayed by itself. A coat of arms is also called an achievement.
Other things sometimes around a shield include the supporters, animals or people on either side holding it up; a grassy mound for it to rest on; and a helmet sitting on top of the shield.
The helmet typically has torn ribbons of cloth hanging from its back (the mantling), and a decorative device perched on top of it. It is this thing, the fal-lal over the helmet, that is the crest.