Subspace (亜空間 Subspace) is a realm central to the plot line of the Subspace Emissary. The realm's general appearance is a mottled, purple-black sky with very little ground (which is also mostly purple), as 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. While inactive trophies and plant life survive the subspacial explosion, it is likely fatal to any living creature, based on how nearby R.O.B.s are torn apart. Once the initial Subspace Bomb detonation is complete, Subspace can be entered by simply walking in these "subspacial bubbles".
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 used the many pieces of the world he collected to create The Great Maze.