He kills all the parts of Tom Riddles soul, and destroys the Horcruxes. Then there is the complicated matter of the Elder Wand. Draco disarms Dumbledore before he can react and before Snape is even there, thus making him the master of the Elder Wand, even if he does not know it. Voldemort thinks it is Snape who is the true master of the Elder Wand so he kills him. Harry takes Draco's wand from him. Thus Harry is the true master of the Elder Wand. Harry and Voldemort are about to duel, Voldemort does not understand properly the magic of wands, and does not listen to Harry's warnings. The both fire spells at the same time, Harry's being "Expelliarmus", considered his signatue move, Voldemort's being "Avada Kedavra", Voldemort is using the Elder wand against it's master, causing his spell to rebound on him. He drops dead.