Currently, the mystery dimension is entitled "The Void" and is accessible while in Creative mode, by flying off the top of the world. The terrain shape is reminiscent of the Nether, or that of the Aether mod. Reaching it in survival mode is difficult but possible through flight abilities such as mage cannon, or whirlwind at higher levels. It is completely unfinished and will be completely changed, and currently features mobs and giant land formations. For now, if you're so inclined, you can explore it, but it is of note that there are currently no dungeons.
Areas and biomes still work in the dimension, though biomes are subject to being removed or changed.
As of 0.5.3, the Area system gets bugged when changing dimensions in SMP, so it's best to avoid the mystery dimension when on a server. If you do travel there, the bug may be fixed by relogging.