The Elder Wand is also known as the Deathstick and the Wand of Destiny.
The Elder Wand does not work properly for Lord Voldemort, as he is not its true master. Voldemort wrongly believes that, as Snape was the one to kill Albus Dumbledore, he is the true master of the wand.
The Elder Wand does not merely belong to the wizard who possesses it; removing it from Dumbledore's tomb did not make Voldemort its master. The Elder Wand recognised Draco Malfoy as its true master after Draco disarmed Dumbledore on the Astronomy Tower. When Harry overpowered Draco, he became master of the Elder Wand.