D&D Monsters: Satyrs

Like centaurs, minotaurs, and harpies, satyrs have their origins in Greek myth. The original versions are wild nature spirits and, in particular, representations of unbridled male sexuality... this survives today in the psychological term 'satyriasis' for uncontrollable sexual desire in men. As with centaurs, this part-bestial nature is represented in their physicality, which combines various animal-like features with an otherwise human, masculine, body.

In later times, the Romans conflated satyrs with fauns, nature spirits from their own mythology that were part-goat part-man. This is quite different from how early Greek art shows them as looking, but it has become essentially universal in western lore since. Nonetheless, since "fauns" lack the rampant sexuality of satyrs, it was their name that C.S. Lewis used in the Narnia books, and his fauns were far more pleasant than Greek satyrs were said to be. Otherwise, "satyr" has generally been the more common term in fantasy, and that's the term that D&D uses.