The moon is a dimension that can be traveled to by spaceship. It was added as part of the mod Galacticraft. There is no air on the moon. So if you want to survive, you must have an Oxygen mask, Oxygen gear, and two of any size Oxygen Tank on the appropriate inventory slots. Otherwise, you will suffocate. Due to the information on the planet menu when you enter space, there is very low gravity on the moon.
There are caves on the moon, like Earth, but they do not open up to the surface. In these caves you could find Tin ore, Copper ore and Cheese ore.
There are even Moon NPC Villages that have their own Alien Villagers. Finding one on the moon is about the same chance of finding one on Earth. Dungeons can be rarely sighted on the moon too. It is made from grey moon bricks and dotted with cobwebs.
If you bring Saplings to the moon, you can make a oxygen bubble and refill your oxygen tanks. To do this you will need a bubble distributor, and make sure to bring some dirt to plant the sapling on.