late 14c., satire, "one of a type of woodland deities part human or animal; demigod or spirit of the air or woods, companion of Bacchus," from Old French satire and directly from Latin satyrus, from Greek satyros, a word of unknown origin. "The etymology of [satyros] is unknown. A number of hypotheses have been proposed, but none of them makes sense ..." [Beekes].
In pre-Roman Greek art, a man-like being with the tail and ears of a horse; the conception of a being part man part goat is due to Roman sculptors, who seem to have assimilated them to the fauns of native mythology. In some English bibles the word is used curiously to translate Hebrew se'irim, a type of hairy monster superstitiously believed to inhabit deserts.
In Middle English the word could mean also a kind of ape supposed to live in Africa or Arabia (late 14c.), after a use of Greek satyros, and the name was later applied by zoologists to the orangutan (1690s). From 1781 as "very lecherous or lascivious person." Related: Satyress.