"Battle Angel" is based on the Japanese Manga series of graphic novels by Yukito Kishiro. The movie combines the first three books, Ido, Alita, and Hugo.
Set in the 26th century, the story takes place 300 years after a societal collapse caused by a major war. In that society, it's a technological dark age following a pinnacle of achievement far beyond where we are right now. Cyborg technology is a way of life. People are augmented a lot as workers, so being a cyborg is not unusual.
The main character is a cyborg. She has an organic human brain, and she looks like she's about fourteen years old. She has a completely artificial body and she's lost her memory. She is found in a wreckage and reconstituted by a cyber-surgeon who becomes her surrogate father.