Like the Hallows, mastering death is also the goal of the Horcrux, a Dark, Dark, super-Dark kind of magical object. However, unlike the Hallows, there's no good way to use a Horcrux. As we learned in Book 6, Harry Potter and the Half-Blood Prince, a Horcrux is a kind of vessel in which an evil wizard stores a part of his soul; as long as that vessel stays intact, the wizard clings to life. The catch is that a Horcrux can only be created by ripping the soul apart by the worst means possible – murder. Voldemort, cold-blooded, snake-faced, casually-murdering villain that he is, has created seven Horcruxes, more than anyone ever has before. As we know, Voldemort really doesn't want to die. Like, ever. And really has no problem with murdering. Bad combo.
A Horcrux can be anything, as we've seen here, ranging from inanimate objects, like a cup or a locket, to living creatures, like Nagini or Harry. The Horcruxes that Voldemort has chosen are symbols of his desires and plans. As one notable example, he's stored three snippets of his soul in relics of the Hogwarts founders, Ravenclaw's diadem, Hufflepuff's cup, and Slytherin's locket. These represent his profound longing to attach himself to the deepest-rooted lineage in the wizarding world, that of Hogwarts School. This desire clearly emerges from his own doubts and fears about his background. As a half-blooded wizard (his father was a particularly unmagical Muggle), the young, pre-Voldemort Tom Riddle chafed at the idea that any part of the magic world might be hidden from him, and the objects he chooses as Horcruxes reveal his deep yearning to master all aspects of wizarding knowledge and life. Each Horcrux thus is a symbol of some aspect of Voldemort's own insecurities, and so it seems fitting that their destruction ultimately brings about his downfall.