In the "Harry Potter" series, there are seven Horcruxes: Tom Riddle's diary, Marvolo Gaunt's ring, Slytherin's locket, Hufflepuff's cup, Ravenclaw's diadem, Nagini the snake and Harry Potter himself. Each Horcrux contains a fragment of Voldemort's soul.
All seven Horcruxes have a personal meaning to Voldemort. The diary belonged to him as a teenager and was the first Horcrux he created. The ring and the locket are both family heirlooms. The locket also traces back to Salazar Slytherin, Voldemort's ancestor and one of the four founders of Hogwarts School of Witchcraft and Wizardry. The cup and the diadem belonged to two of the other founders, Rowena Ravenclaw and Helga Hufflepuff. These were important to Voldemort because Hogwarts felt like his home, and it's where he began to learn magic. Nagini the snake was Voldemort's pet. He used her venom to regain his strength. Harry Potter became a Horcurx when Voldemort tried to kill him as a baby. Voldemort was unaware that Harry was a Horcrux.
Horcruxes are an attempt to obtain immortality. They are created with dark magic and murder. When a wizard commits murder, a part of his soul breaks. That part can be hidden in a Horcrux so the wizard never fully dies unless that Horcrux is destroyed also.