As summed up in the article about The River Without End,
Each iteration of the universe ends when the River presses in on the universe until it is compressed into a single point of infinite density. A new iteration of the universe begins when the universe explodes outward against the River, expanding until it has reached some semblance of its former shape.
The world during each iteration is geographically identical to The Real World.
The world during the pause between iterations, called Eden, is quite different:
Eden extends outward from the innermost area (“The Garden”) through several rings of disparate biomes until it reaches the desert at the edge of existence. The desert region is itself surrounded by The River Without End.
The land itself is also divided into regions whose borders cut across the various biomes. In the song “West of the Reek” by E. Christopher Clark’s band Pop Bubblegum Trash, travelers are advised by The Ghost to “stay north of Wonderland and west of the Reek” and to “stay south of Narnia and east of land of Oz.” The Garden itself appears to be the only “safe” space.