Coxcomb is a noun - an archaic term for a vain and conceited man; a dandy; a fop.
The term was also used for a jester's cap. Such caps were often decorated with a piece of red cockscomb. In Medieval times such caps usually had three points representing the ears and tail of a donkey that jester's wore in earlier times.
Thirdly, the word is still in use as a variant spelling of cockscomb - the fleshy red crest on the head of the domestic fowl and other gallinaceous birds.
The adjective from coxcomb was coxcombical or coxcomical, meaning foppish or conceited. In 1755, Dr Johnson described coxcomical as a 'low word unworthy of use'. That's a shame - I think it's a wonderful word and wish it were still in common usage.