I can't believe I had to go to Wikipedia to get this:
********************************************************
Harry, as a baby, was the only living entity left in the room when Voldemort's fatal Killing Curse backfired on himself. Voldemort's soul had been so weakened and unstable by his continuous creation of Horcruxes that when he was ripped from his body, a fragment of his soul was lost when he fled the scene which attached itself to Harry. This gave Harry a window into the Dark Lord's mind and his gift of Parseltongue. It also explains the Sorting Hat's inclination to place him in Slytherin House.
Years later, Voldemort used some of Harry's blood to resurrect himself, as described in the fourth book. As a result, some of Lily Potter's protection over Harry was in Voldemort. This accounted for the "gleam of triumph" in Dumbledore's eyes upon learning that Voldemort had used Harry's blood in the fourth book, knowing that it was this mistake that would save Harry--by bringing Lily's sacrifice of love into himself, Voldemort had in effect turned himself into a Horcrux for Harry, in that Harry could not die until after Voldemort did himself. Unlike the other Horcruxes, Dumbledore did not directly suggest to Harry that he could be a Horcrux; he asked Severus Snape to reveal this information to Harry at the end of his task, hoping Harry would have summoned up enough courage from his previous adventures to sacrifice himself willingly, though Dumbledore suspected and hoped that the blood connection would keep Harry from actually dying. In dying willingly, Harry ensured that when the connection was eventually broken and both he and Voldemort were mortal, he would still be the master of the Elder Wand and thus be able to defeat the Dark Lord.
Voldemort was entirely unaware that Harry was his seventh Horcrux, or the fact that, by giving himself Harry's blood, he had actually made it harder to kill Harry. Thus the curse did not destroy Harry, but did, however, destroy the piece of Voldemort's soul inside him; as a result the two's magical connection was broken, and the way was cleared for Harry to kill Voldemort later.
********************************************************
Source I still don't like it... but at least now I get it...