Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort's soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsing building. Part of Lord Voldemort lives inside Harry, and it is that which gives him the power of speech with snakes, and a connection with Lord Voldemort's mind that he has never understood. And while that fragment of soul, unmissed by Voldemort, remains attached to and protected by Harry, Lord Voldemort cannot die.
— Harry Potter and the Deathly Hallows
by J.K. Rowling