The story of Adam and Eve forms the basis of the Christian creation myth. After God created the Earth, he created Adam in his own image (the first man). God then removed one of Adam's ribs and from it he created Eve (the first woman). Eve in turn became Adam's wife. The two were given dominion over the Garden of Eden (paradise), until they were coerced by Satan to eat fruit from the Tree of Knowledge, which granted them the knowledge of good and evil. As a result, God banished Adam and Eve from the Garden of Eden.
Interestingly enough, the only mention of Lilith in the Christian Bible is in Isaiah 34:14, which refers to her as a demon (she is also often referred to as a night creature or screech owl, depending on the translation). The origin of Lilith traces back to Judaic mythology. The Alphabet of Ben-Sira, written sometime between the 8th and 11th centuries, is one such medieval reference.
In it Lilith is described as the first woman created by God, and Adam's first wife. However Lilith refused to assume a subservient role to Adam, instead seeing herself as his equal. One such argument occurred during sexual intercourse when she said, 'I will not lie below,' and to which Adam replied, 'I will not lie beneath you, but only on top. For you are fit only to be in the bottom position, while I am to be the superior one.'
In response Lilith invoked the name of God and took off into the air, leaving the Garden of Eden and deserting Adam. She settled near the Red Sea, where she mated with demons and gave birth to countless Lilim (her offspring—also considered demons).
Adam asked God to return Lilith to him, and three Angels were sent to retrieve her. The Angels threatened to kill one hundred of Lilith's demonic children each day that she did not return, to which she countered that she and her children would forever prey upon the descendants of Adam. They eventually struck a bargain in which Lilith would spare any child that was under the protection of the Angels. However she would still not return to Adam.
When it became apparent that Lilith would not return, God created another woman, this time in front of Adam. The creation process disgusted Adam to the point that he could not bare to look at her, forcing God to take her away. Finally, while Adam was asleep, God removed one of his ribs and from it he created Eve. When Adam awoke and saw Eve before him, he fell in love. The two lived happily in the Garden of Eden until they consumed fruit from the Tree of Knowledge, thus rebelling against God and causing the fall of mankind.
The myth of Adam and Lilith is used as an inspirational reference in Neon Genesis Evangelion, not necessarily a literal one. In the series they are equal beings considered to be the Progenitors of Life. While the Angels are descendants of Adam, the Lilim (humanity) are descendants of Lilith.
Possibly one of the most controversial aspects of the show is it's reference to humanity as Lilim—or demons. In Christian and Judaic scriptures demons are always portrayed as evil beings to be feared or avoided by humanity. While the show does project the idea that it is humanity that are the Lilim, it does not necessarily label Lilim as demonic or evil. Neither however, does it label the Angels as such.
Considering the mythology of Adam and Lilith, one can make the argument that the Angels are simply attempting to rescue (or be reunited with) their progenitor Adam, who was captured and imprisoned by the Lilim, the demonic children of Lilith, who would use him for their own purposes. The Lilim on the other hand may be demons attempting to artificially reach the evolutionary level of an Angel via the Human Instrumentality Project. Such a plot in itself would not be controversial if not for the final revelation that it is in fact humanity that are the Lilim, and the story is told from their point of view.
That is however one of many interpretations. The fact remains that while Neon Genesis Evangelion has many religious references, most are only used for inspirational purposes. Director Hideaki Anno himself has stated that the show should not be taken that seriously, and that the only reason he chose Judeo-Christian concepts as the backdrop for the show was because Christianity was at the time a very mysterious religion in Japan, with less than 1% of the population practicing it. The genius of Evangelion is not that it offers some new revelation about God or life, or that it deconstructs past religious concepts into something more. The genius of Evangelion is that it makes people think about such concepts in the first place.
Lilith today is often considered as the first feminist, and male-dominated religious institutions of the world are blamed for demonizing her. Some feminists also dismiss the myth that man was created first, forcing a chicken-or-the-egg argument between the sexes. Ironically, modern science shows that a human fetus is conceived in female form, and is not affected by the male chromosome until some time into the pregnancy.