Despite the fact that he repeatedly tells Lily she doesn't have to die, Voldemort kills Lily to get to Harry and then casts the Killing Curse, "Avada Kedavra," on the baby. The curse rebounds ...
That's why Harry survives Voldemort's initial Avada Kedavra curse, but Narcissa is the reason the Dark Lord doesn't strike Harry with a second one. After he and Harry recover from the first ...