Rei Ayanami is name of the human shaped avatars created for Lilith, an abomination from deep space once hellbent in the eradication of all life in Earth to force a new beginning. Each of these avatars house part of Lilith's essence, and some of them even have personalities and memories of their own, but also work as a hivemind, sharing information and able to combine as one and become the the original Lilith again whenever needed in a flash. These avatars were created by the Gehirn organization (later renamed to Nerv) and some of them even used to pilot one of their also Lilith based bioweapons, the Evangelion Units, but she has long broken any ties to them and is no longer under anyone's control.
However she hasn't resumed her onslaught, and is no longer interested in ending the World as humans know it. The experiences of the whole Ayanami series and the fact that the base woman for creating Lilith's human avatars had fragments of her subconscious diluted into each and every one of them have changed Lilith's intentions. Despite being able to drive any human into madness and turn them into the primordial soup some call LCL, she decided to use her reality bending abilities to escape her own and into this one. Her intentions and the state of her reality before she left if behind are unknown, but no part of her (or the sum of them all) appear to be hostile. What does she want? And what experiences and events does she carry inside?