Guardian Deity
The Four Giants are the guardian gods of Termina that rest in the four cardinal directions of the land of Termina: Woodfall, Snowhead, Great Bay and Ikana Canyon. They were, however sealed in four monsters: Odolwa, Goht, Gyorg and Twinmold, by the evil inside Majora's Mask. Because of this, the four domains became cursed and the creatures living near the temples were afflicted by troubles. However, the most devastating curse was inflicted on Clock Town, with which the Skull Kid had summoned the Moon to collide. However, Link saved the Giants by defeating the curses they were trapped in, and with the Oath to Order, called the four Giants to stop the Moon from falling.
It is possible that Odolwa, Goht, Gyorg, and Twinmold are actually their names, as in the manga the Deku are said to worship Odolwa, although in both the game and the manga their Woodfall Temple is dedicated to the Southern Giant, and the Odolwa boss is clearly hostile to them.
It is further possible that the four bosses are alternate forms of the Giants that have merely been driven to evil. (For example, the Western Giant would not do well out in the ocean as a relatively tall being, and "Gyorg" is associated with other fish beasts in the series)