Moon

The Moon was a puppet of Majora's Mask during Link's adventure in Termina. By the power of Majora's Mask, it had been pulled from its orbit, threatening to crash into Clock Town, which would obliterate the town, along with most of Termina.

One of the interesting points of the moon is that it always faced south. The Moon also has the same eyes as Majora's Mask, perhaps due to the curse put on it. Another thing is, is that either inside or on the surface of the Moon is a beautiful meadow, hazy like a dream; the only thing to break the scene was a single tree. The moon was stopped from its path by the Four Giants, after Link freed all the giants he played Oath to Order beseeching the Four Giants to come to the aid of the people of Termina. The moon then became possessed by Majora's Mask, which manipulated it into opening its mouth, its eyes started to glow, and it said:

"I- I shall consume... consume- consume everything"

- Moon

The moon was the scene of the final battle in the game, and it seems that it was destroyed afterwards. The moon was one of the many mysteries of Termina that will probably never be solved. However, if you fail to find the Four Giants in time, the Moon will destroy Clock Town and possibly most of Termina.

The Moon's Face
The Moon's menacing face is as small matter of debate. The main argument is to its existence - does the Moon actually have a face, or the menacing visage a metaphor to the impending doom over Termina? Perhaps the Moon's face is an intimidating curse of Majora's Mask - an argument which has been put forward due to the similarities between the eyes on the Moon and Majora's Mask. It is interesting to note that the Moon's face is never referenced within the game - perhaps the people of Termina are used to the Moon having a face, seeing it as nothing unusual - or perhpas the face is simply a metaphor, only to be seen by the person playing the game. Either way, the Moon sharing the same eyes as Majora's Mask is likely to be symbolic of the curse held by Majora's Mask.

Other games
In the Wind Waker, in the Nintendo Gallery, there was a sculpture of the moon in the background behind the counter.

In Super Smash Bros. Melee, the stage "Termina: Great Bay" had the Moon from Majora's Mask in the background. As the match continued, it would slowly descend (not affecting the match in any way). The Four Giants would also come and push the Moon back up. There was also a trophy of the Moon that could be collected in the game. It's trophy bio states that in the Moon is a plain with a broken tree.