There have been many versions of Lilith's story told over the ages. Some say she and Adam started out as one person, but then God split them in two, creating two people, while others say that she was, like Adam, created from clay (rather than being made from one of Adam's ribs).
In either version, Lilith is said to be a spirited woman who refused to be subservient to Adam, which resulted in her expulsion from the Garden of Eden. After she left, God created Eve to be a companion for Adam. (In some texts, Adam is also said to have a second wife before Eve.)
From there on, some say that she went on to travel the road between worlds, preferring the company of angels and demons, with many of whom she mated and bore children.
The Jinn race was said to be descended from Lilith's children.