"rustic woodland spirit or demigod part human, part goat," late 14c., from Latin Faunus, the name of a god of the countryside, worshipped especially by farmers and shepherds, equivalent of Greek Pan. The faunalia were held in his honor. Formerly somewhat assimilated to satyrs, but they have diverged again lately.
The faun is now regarded rather as the type of unsophisticated & the satyr of unpurified man; the first is man still in intimate communion with Nature, the second is man still swayed by bestial passions. [Fowler]
The plural is fauni. The word is of uncertain origin. De Vaan suggests Proto-Italic *fawe/ono-, from a PIE word meaning "favorable," with cognates in Old Irish buan "good, favorable; firm," Middle Wensh bun "maiden, sweetheart."