The Dream World is a realm past the everyday Waking World, just a bit deeper past normal dreams. It exists as both a dream and a reality, and can be interacted with and lived in just like the Waking World.
There's a variety of ways people can visit it. Most commonly, tourists wind up there by sleeping at important points in their lives or in unusual places.
The story follows Nada after they wake up in the Dream World right as catastrophe hits – the teleprisms that let people teleport to and from the Dream World disappear. Taffy, who is assigned as Nada's Dream Guide, leads them through the Dream World trying to get them back home.