How Did Harry Die?
He Was Hit with a Killing Curse That Sent Him to Limbo, but It Wasn't Harry Himself That Died. to Understand This Answer Properly, We Have to Go Back and...
He was hit with a Killing Curse that sent him to limbo, but it wasn't Harry himself that died. To understand this answer properly, we have to go back and explain why and how Harry was turned into a Horcrux which required him to “die” by Voldemort's hand.
How does Harry Potter die?
He split his soul into seven fragments called Horcruxes that could've allowed him to live forever if they weren't destroyed. Throughout the series, Voldemort sets out to kill Harry Potter because of a prophecy that predicted Harry would defeat him.
Why did Harry Potter die?
Voldemort carried Harry's blood within him, and thus carried Lily's protection. He was a sort of tether that bound Harry to the real world. So when Voldemort “kills” Harry in DH, the piece of Voldemort's soul inside of Harry was killed for real (given that it was not protected by Lily's magic).