This feature was exclusively part of a joke version and is not currently planned for addition to regular Minecraft. It is documented here on the wiki due to being officially-released content by Mojang Studios, even if not present in a final version.
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The Moon is a joke dimension that can be accessed by flying up to Y=700 in the Overworld.
The Moon has a weak gravitational pull. So weak, in fact, that at certain heights the player will be pulled back to Earth, "falling up", so to say. The player's oxygen also decreases on the Moon, though much slower that in water. Cheese, which makes up almost the entirety of the Moon, restores both hunger and oxygen, allowing the player to survive here.
The Moon can be accesed by flying up to Y=700 in the Overworld. Conversely, flying up to Y=700 in the Moon will bring the player back to the Overworld.