The Elder Wand is the tail hair of a Thestral; a powerful and tricky substance that can be mastered only by a witch or wizard capable of facing death.
After killing a rival wizard in a duel shortly after obtaining the wand, Antioch drunkenly boasted of the wand's powers. He was murdered in his sleep that night, and another wizard took possession of the wand. Over time, the powerful wand passed through various owners, usually in violent circumstances, and acquired names such as "The Deathstick" and the "Wand of Destiny."
It eventually ended up in the ownership of the wandmaker Gregorovitch, who was trying to duplicate its powers. It was stolen from him by the Dark Wizard Gellert Grindelwald, who used it to cause havoc in Europe until he was defeated by Albus Dumbledore. The ownership of the wand then passed to him. Many years later, Severus Snape killed Dumbledore, who requested that Snape kill him to save him from a more agonising death, and because this act was agreed on, Dumbledore would not be 'defeated', so the powers of the elder wand would be nullified. This led Voldemort to believe ownership of the wand was Snape's.