The Shivering Isles, also known as Sheogorath's Realm of Madness, or simply The Madhouse, is a realm of Oblivion included in The Elder Scrolls IV: Shivering Isles expansion. It is Sheogorath's Plane of Oblivion. The realm consists of three parts: Mania, Dementia, and The Fringe.
Getting to the Shivering Isles
Arrival to the Shivering Isles is solely at the discretion of Lord Sheogorath, Prince of Madness. He permits you access after killing an insane dark elf that comes out of the portal to the isles. Once you kill him you can enter the portal.
The best way to explore the Shivering Isles is by foot. Take the time to meander along the paths that stretch across the beautiful landscape. A weary traveler can often find a place to rest at one of the many campsites found dotted across the world. But those campsites are often filled with mages that worship Sheogorath. Keep in mind that creatures roam freely here just as much as they do in Nirn, so it won't exactly be a walk in the park.