Horcruxes were multiple souls found in the Harry Potter series. They were found when people (most commonly known, Lord Voldemort) would split their souls into pieces using magic and hide them in different objects. This way, they would live much longer. In order to kill the person, you would have to destroy all of the horcruxes first. You could not destroy them with a simple magic spell, they needed to be destroyed with something more powerful. Harry destroyed the horcruxes with the Sword of Gryffindor.