An empty-headed, vain person. The ancient licensed jesters were so called because they wore a cock's comb in their caps.
Coxcombs, an ever empty race, Are trumpets of their own disgrace.
Gay: Fables, xix.
“Let me hire him too; here's my coxcomb.”
Shakespeare: King Lear, i. 4.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894