In Tolkien's mythology, Durin the Deathless was set to sleep beneath the mountains of Middle-earth until the Elves were born. The name Durin, like all other names of Tolkien's Dwarves, was taken from old Norse: this was later explained by the translation fiction: because Westron was translated with English, the language of Dale had to be translated with Old Norse. The Dwarvish names were in Dalish, which was translated in The Hobbit and The Lord of the Rings with old Norse.
Upon his awakening in the First Age, he traveled until he came upon the Mirrormere, the lake that the Dwarves call Kheled-zâram. He created there a great city within the Misty Mountains. This was Khazad-dûm, later called Moria.
Durin founded the line of Dwarves called Durin's Folk, the inhabitants of Khazad-dûm. Durin was called the Deathless because he was believed not to die, but rather to fall asleep, and reïncarnate in his own line. The Dwarves of Durin's folk were ruled by six kings named Durin, all fathers and sons, until Durin VI, who was killed in 1980 of the Third Age. After him Durin did not return to his people for many years, until in the Fourth Age a Durin VII appeared, son of Thorin III, grandson of Dáin II Ironfoot, and descendant in direct line from Durin the Deathless. Durin VII was known as Durin the Last.
His birth was prophesied at the Battle of Five Armies, and he led Durin's Folk back to recolonise Khazad-dûm during the Fourth Age, where they remained 'until the world grew old and the Dwarves failed and the days of Durin's race were ended.' (According to The Peoples of Middle-earth, "The Making of Appendix A (iv): Durin's Folk".)