We have been reminded multiple times throughout the course of the Harry Potter series that what saved him from Voldemort when he was a child was his mother's love. In the Goblet of Fire, Voldemort even tells his death eaters that this was the reason. However, why is it in the Order of the Phoenix, Lucius tries to tempt Harry and tell him that if he hands over the prophecy, he will find out what saved him that day?
Lucius is not known for his honesty. As this does not happen in the book, the movies probably added this in. If Harry had given it to them they would have killed him, not given him any information.
So. To answer your title, his mother's sacrifice.
I don't quite remember the scene where Lucius Malfoy telling the
"Lucius tries to tempt Harry and tell him that if he hands over the prophecy, he will find out what saved him that day?"
This is not included in the book. However, there is some similar line to this that Lucius said to Harry. But, I am under the impression that Lucius was trying to say what saved him that night when Voldemort tried to kill him.
Overall, it was his mother's love and sacrifice that saved him. It is the reason why he also didn't die in the Forbidden Forest. (Including a bit of Voldemort's soul)