The Dream World, also called The Dreaming or the Dream Realm, was an illusory realm that an individual could at times enter when he or she fell asleep.
Here, dreams were constructed by the master of dreams himself; Morpheus.
Sleep was a demon who also apparently had some sort of power in the Dream World, although his power over it wasn't absolute as Morpheus' power was. After all, he was imprisoned for a billion years before 1983, when Superman accidentally released him.
He was placed back in his prisoncontainer of alien origin, which presumably cut off his control of the Dream World completely, making it fully under the control of Morpheus yet again.