The Moon is a celestial body, the only natural satellite of Earth. During the events of Katamari Damacy, the King accidently destroyed it while out on a bender. It is the last object that the Prince needs to collect items for. After a new Moon is created, it is used as a special Katamari in the Credits bonus game.
The Moon is destroyed by King during the intro of the game. After the Prince has made all the other stars in the sky, the King sends him to roll up a 300m Katamari. Once the Prince completes this challenge, it is placed in the sky where the old one was.
The minimum size of the katamari is 300m, while the largest possible (seen so far) size is 906m. If the Prince can roll up an 800m katamari before time turns out, it unlocks Eternal stage 3.
During the credits, the Moon is used as a katamari to roll up all the countries on Earth, 195 in all. The number of countries collected by the katamari does not change anything else in the game, and a high score is not kept.
Dipp can be found in this stage, sitting behind the podium in the school yard at the edge of town. Watch out for the people running around in circles. He dissapears at 12 meters, I think. The present for the stage is the Cool Mask.
The Moon can be seen orbiting the Earth in the Cosmos during the Roll up the Sun stage. It is quite easy to roll up as the first item on the katamari. If the save data from Katamari Damacy is transferred to your save file, the Moon will be slightly bigger and glow brighter depending on how big the katamari from the first game was.
It is later used to once again collect the countries in an unlockable stage, this time creating a new planet for the Cosmos. It does not look any different if save data is transferred.
The Moon is created in the first stage of the game, Egg School. After the Moon is made, up to 9 extra moonlettes can be made that will orbit the Moon in the Cosmos.
Katamari Damacy's Make The Moon stage reappears in this game. The credits game, however, does not.