The Giant is one of four similar magical giants collectivly called "The Four Giants" which exist in the land of Termina. They are orange-colored, have beards and resemble large heads with long legs and arms. They are responsible for the creation of the four regions of Termina that surround Clock Town. After the giants made the four regions they left Clock Town to live with their races that lived in those regions. They were close friends with the Skull Kid, but got angry with him when he played tricks on others. In Majora's Mask, the Skull Kid, under the influence of Majora's Mask seals away the Four Giants in evil masks, manifesting as monsters that harm their own regions. Link must free them so they can stop the Moon from crashing into Termina. At the end of the game, they reveal that even though they left the Skull Kid, they hadn't forgotten him.
Source: Wikipedia, "http://en.wikipedia.org/wiki/Characters_in_The_Legend_of_Zelda_series," available under the CC-BY-SA License.