The Dream Realm is one or many domains of unconscious reality encountered in various forms in Martian Dreams, Ultima Underworld II and Ultima VII Part Two. A person's psyche may be quite literally transported there whilst in a slumber, whether natural or induced by other means. It has generally taken the appearance of large, floating landmasses or pathways and often contains dream analogs of actual environments found in the physical world. Other people may be found there simultaneously experiencing their own dreams and can be veritably interacted with as if they were face-to-face.
In Martian Dreams, the Realm was accessed through the Dream Machines. The Martian race had fled there and the Avatar undertook the task of defeating the evil Raxachk, who had taken control over it. It was also there that the Avatar found a way to destroy him.
Its presence in Ultima Underworld II was somewhat more figurative, appearing as a way to interact with the Ethereal Void itself. Eating a Dream Herb and sleeping would induce a dream vision of the Shrine of Spirituality. The Avatar then travelled there physically—even as others found there persisted in a state of dreaming—through the Blackrock Jewel in order to destroy the Guardian's place of power and find a Blackrock Gem, all the while overcoming dangerous Gazers, Daemons and Brain Creatures.
In Ultima VII Part Two, the Avatar was transported to the Dream Realm through a rift in Gorlab Swamp and liberated the souls of the inhabitants of old Gorlab from the tyranny of the evil mage Rabindrinath, enabling passage through the boggy marshes upon reawakening.