Lilith is a female "demon" of Jewish folklore; her name is related to the Babylonian-Assyrian demon called Lilit, or Lilu. There are a few variances in her myth, but most commonly, she is said to have been Adam's first wife, but after refusing to let him have the superior sexual position, she was banished from the Garden and later became some kind of nightstalker that preyed on babies and men, giving birth to demon children according to some traditions, sterile according to others. (Her sterility is supposed to be her motivation to kill babies and men.) One theory is that it was Lilith who sent the serpent to Eve and started all that trouble in the first place.
Anyway, Lilith has become a feminist symbol for her rebellion against the patriarchal system. It is interesting to note that both Lilith and Lucifer have in common the act of "rebellion", or rather, questioning why someone has to be superior to another, and both were demonized for it.