Depending on how you read things, Lilith is…

• Adam’s first wife, who fled Eden rather than submit to him, never Fell, and sort of became a demon who’s responsible for crib-death.
• the remnant of some proto-Hebrew Mother Goddess, who got demonized when Yahweh got all pissy about being the One And Only God.
• the female half of a demonic male/female pair that mirrors Adam and Eve – her husband is one Samel. In this version she may or may not be, or have begun as, a sort of conjoinment with Samel, and Adam and Eve begain as one conjoined being as well.
• the result of several generations of half-mad Kabbalist scholars taking one line in the Bible a bit too literally and creating a myth to explain it out of next to nothing.

Religion is funny that way.

Text from Kabbalistic literature, and a ritual for summoning Her.