Lilith was supposedly Adam's first wife before Eve. It's said that Lilith was made at the same time and of the same earth as Adam was. They lived together in the garden until Lilith had refused to submit to Adam and fled from him to the sea. The most common guess of which sea is either the Red Sea or the Dead Sea. It says that Adam pleaded to God to bring her back to him, and so God made an attempt to. He sent three angels to Lilith's location where they told her that they would kill 100 of her demon children a day, Lilith was thought to be a lover of demons, if she did not return to Adam. Lilith refused saying that she was made for hurting infants (young children). Another version says that she took the lives of the children because she was receiving revenge on God for taking her children's lives. She did have to swear though that if she saw the three angels names that God sent: Senoi, Sansenoi, and Sammangelof, the names may vary. Thus, childbirth 'amulets' against Lilith were made to protect the child and mother from her.
These 'amulets' came in several different forms. Some only had the three angels' names on them, but some had the three angels' names with their structures, wings, legs and hands. Another version was of Lilith bound in chains. Other version may have actually have the one of the stories of Prophet Elijah on it. This story goes that one day Elijah ran into Lilith and asked her what she was doing. She wasn't able to lie to him or avoid him, so she told him she was on her way to a woman's house, who was going into labor, "to give her the sleep of death, to take her son and drink his blood, to suck the marrow of his bones, and to eat his flesh" (some versions say "to leave his flesh"). Elijah cursed her, but Lilith made a deal that if he freed her, she would give him all her names. She promised that if she saw or heard these names she would leave the mother and child alone.
There are many different variations of the story of Lilith. One even accuses her of tempting or assisting in tempting Adam and Eve. But, whatever story seems to have in common is that she is "the strangler of children" and that she seduces men. Causing her to bare more demonic babies. She's often listed as one of the most popular of the four demon mothers. The other three being Agrath, Mahalath, and Naamah. They are also sometimes referred to as the four daughters of night. Though, sometimes Lilith is just said to be a common succubus.