The Elder Wand is said to be indestructible but, like everything, it has its limits. The wand was used in a massive battle between Voldemort and Harry Potter and was damaged as a result. It broke because it was restricting the energy from the spells being cast. Although Voldemort was powerful, he wasn't the wand's true owner, so the wand wasn't able to perform the spells to its true strength. The turmoil caused it to crack.