Subspace
Subspace is a realm central to the plotline of the Subspace Emissary. The realm's general appearence is a mottled, purple-and-black sky with very little ground (which is also mostly purple). Lightning laces the sky.
Subspace is enforced on the World of Trophies by Tabuu. Over the course of the Subspace Emissary, Subspace Bombs are used to remove portions of the world, drag them into Subspace, and leave a patch of Subspace behind. Subspace can be entered by simply walking in these "subspacial bubbles" once the initial Subspace Bomb detonation is complete. (While inactive trophies and plant life survive the "trip" into Subspace, it is likely fatal to any intelligent being.)
Once a piece of the world has been shunted into Subspace, it floats around as a "colony". The colonies are then shut off from the rest of the world, Subspace and otherwise, unless a connection is made between the colony and either Subspace or another colony. Tabuu uses the many pieces of the world he collected to create The Great Maze.
This Subspace is different from the Subspace of Super Mario Bros. 2. However, it is (visually) very similar to The Void of Super Paper Mario.