The Moonbase was a structure built on Earth's moon by Project Binary during Act 4 of Destroy the Godmodder 2. During the End of Act 3, Binary had flung a missile at TwinBuilder that contained a portion of his consciousness. TwinBuilder evaded the attack, and the missile had crash-landed onto the moon instead. The missile gained true sentience, building the Moonbase around itself for protection.
The Moonbase grew to become a factory for Project Binary's spaceships, and as a prison for any and all Minecraft players Binary encountered on Earth. The presence of an effective second Project Binary (contained within the Artemissile, at it was to be called) also boosted Project Binary's mind control powers even further, securing his hold on Earth. The Moonbase was destroyed in the End of Act 4, when the almost-destroyed Artemissile used it to fling the moon into the Earth, shattering the universe. Once the universe was restored in Act 5, the Moonbase was vanished from existence.