In the last movie, Harry was struck by the Avada Kedavra spell cast by Voldemort. Really, he should be dead. But obviously he was not dead because when Narcissa Malfoy (Draco's mother) asked about the life/death of her son, there was a pause hinting that Harry was talking to the woman. And knowing Malfoy is not dead, in return, the woman declared Harry was dead.
However, one should really be dead if struck by the Avada Kedavra spell. Does this indicate the work of the Resurrection Stone?
No, Harry dropped the Stone before his encounter with Voldemort in the Forbidden Forest.
If he survived, it's because :
When Harry met Voldemort in the Forbidden Forest, Voldemort used the Killing Curse on him almost immediately, but only destroyed the Horcrux, rendering his scar "normal." What was not revealed to Voldemort was that when he used Harry's blood three years prior to gain himself a new body, the blood passed Harry's mother's protection to Voldemort and anchored Harry to the living world through Voldemort. Harry was merely knocked to the ground and feigned death. Voldemort, as a result of destroying his soul shard in Harry, was also knocked out
- Harry Potter wiki, "Tom Riddle" article, "Final battle and death" section
Harry Potter clearly did die. This is clear from, for example, the discussion revealed in Snape's memory between Snape and Dumbledore where it is explained to Snape that the only way to defeat Voldemort is for Potter to die.
What is not clear is how Potter comes back as neither the book nor the movie make any attempt to explain it. But his death is clearly necessary for Voldemort's defeat.
Harry Potter did not die. Instead of killing Harry, Voldemort's Avada Kedavra killed the piece of his own soul that was attached to Harry and that made him the seventh Horcrux. Obviously the spell was powerful enough to nearly kill Harry as well, but as Dumbledore says, "Voldemort has clearly always underestimated the power of an intact soul". Harry had a choice at "King's Cross"; he could head back to the world of the living and try to make a difference, or he could "take a train". Harry's will to finish the fight led him to choose the former.
After the Killing Curse hit him, Harry asks Dumbledore if he’s dead, and Dumbledore says no.
“Then … I’m dead too?’
‘Ah,’ said Dumbledore, smiling still more broadly. ‘That is the question, isn’t it? On the whole, dear boy, I think not.’
They looked at each other, the old man still beaming.
‘Not?’ repeated Harry.
‘Not,’ said Dumbledore.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
The reason for this, Dumbledore goes on to explain, is that the Dark Lord taking his blood tethered him to life while the Dark Lord lived, since Lily’s protection was then inside them both.
“He took your blood believing it would strengthen him. He took into his body a tiny part of the enchantment your mother laid upon you when she died for you. His body keeps her sacrifice alive, and while that enchantment survives, so do you and so does Voldemort’s one last hope for himself.”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
Harry’s blood in the Dark Lord tied him to life, so he didn’t truly die. He was further helped by being the true master of the Elder Wand. It didn’t want to kill its master, so the Killing Curse it cast against him wasn’t as powerful as it could have been. It had nothing to do with the Resurrection Stone - that only brings back the “shadows” of people who are already dead, it doesn’t prevent death.
As Dumbledore explains to Harry while in "King's Cross", Voldemort made seven Horcruxes (soul was split into 8 parts, including voldemort's own body). The last one he never intended to make, and that Horcrux was Harry. So, rather than killing Harry, Voldemort unintentionally killed the Horcrux he never meant to make.
He was shot with Avada Kedavra, but he never died. Voldemort had killed a part of himself.
Harry possesed the 3 Deathly Hallows. He was the master of death, and thus he could chose to come back to life.
