E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
means one who puffs out his cheeks, and makes a ridiculous explosion by causing them suddenly to collapse. This being a standing trick with clowns, caused the name to be applied to low jesters. The Italian baffare is to puff out the cheeks for the purpose of making an explosion; our puff. (Italian buffone, a buffoon; French bouffon.