The Horcrux is an awful piece of magic. It is a way to insure that even if your body is destroyed, you can live on as a husk of your former self, not many prefer this to death. Horcruxes are made by splitting your soul, and encasing it in another object. The most well known user of them is Lord Voldemort. He had seven. It is very difficult to destroy a horcrux. You can destroy one with a basilisk fang, a goblin made sword, or fiendfyre.