Harry Potter was tethered to life. When Voldemort took Harry's blood in the Graveyard in 1995, he took in Lily's protection, meaning that Harry's blood ran though his own. While Voldemort lives, Harry cannot die. Harry had the choice of coming back to life to finish off Voldemort because technically, part of Harry still was alive. However,both of them did not know this.
Here is a quote on the Harry Potter Wiki,
"What neither he nor Voldemort realised, however, was that when Voldemort used Harry's blood in his resurrection in 1995, he unwittingly took Lily Potter's magical protection of Harry into himself as well, thereby tethering Harry's life to his own."
The statement can be found here, under History, second line.
This is why Harry did not die in the Forbidden Forest.