For questions about "Horcruxes" in Harry Potter in which a person has concealed part of their soul, thus making that person immortal whilst the Horcrux is still intact. Always use with the [harry-potter] tag. Use [voldemort] as needed when referring to those created by the character.
Horcrux is the word used for an object in which a person has concealed part of their soul. First the soul is split by committing a murder, and then the partitioned piece of the soul is hidden in an object outside the body. If one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged.
Note that Harry Potter did hold a part of Lord Voldemort's soul, but was technically not a Horcrux. For a detailed write up on this, see the SFF Blog post about it.