The term horcrux is an invention of J.K. Rowling, first mentioned in the sixth Harry Potter novel, Harry Potter and the Half-Blood Prince. Creating a horcrux occurs when one rips the soul by committing an intensely evil act, such as murder. The portion of the soul ripped away is then encased in some type of meaningful object. Thus, if the physical body of a person with a horcrux were destroyed, the person would still not be dead, unless horcrux containing the piece of soul was also found and destroyed.
Rowling uses the term to explain why Voldemort managed to survive a backfired killing curse when he attempted to kill the one-year-old Harry. Much of the sixth book deals with Headmaster Dumbledore instructing Harry on the horcruxes that Voldemort likely created. These horcruxes kept Voldemort alive, though lacking in a body until the end of Book Four, Harry Potter and the Goblet of Fire.
Through the sixth book, Harry learns that of all places most dear to Voldemort, Hogwarts, the school of witchcraft and wizardry, was the most so. Thus, objects from the school founders are likely places for Voldemort to conceal horcruxes. Dumbledore also suggests that Voldemort created not one horcrux, but more likely seven. As a result, Harry’s final goal is not only to vanquish Voldemort, but to destroy the remaining horcruxes as well.