Majora is trapped inside Majora's Mask. He took over the body of Skull Kid, who stole it from the Happy Mask Salesman. After equiping the mask, Majora takes complete control.
He calls the Moon to fall onto Termina against it's will. It is said that only The Four Giants can stop the Moon and save the world, but they have been sealed in the 4 temples. Link free's The Giants and they hold the moon.
At this point, he decides Skull Kid is too weak for him, so they seperate and he flies into the moon, making it fall harder. The Four Giant struggle to keep the moon up when Link goes inside of it.
There he finds 5 children. Four of them are skipping around a tree and wearing the masks of the games four main bosses. The last one sits beneath the tree alone. If Link talks to him, he asks if Link would like to play with him. If he answers yes, it triggers the final battle.
In the final fight with Majora, he has three forms:
Here he is basically just the mask, but all floaty. Several tentacles also hang out from the back.
In this form, he has sprouted limbs and a single eye with horns. He jumps around and dances.
This is the final form. His limbs have become beefier, and he now has a head.
At the start of this fight the masks of Odolwa, Goht, Gyorg and Twinmold float and attack. They die fairly easily though.