Currently, the mystery dimension is entitled "The Void" and is accessable 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. A reliable way to reach it in non-Creative has yet to be found (though you can jump in and out of it by making block towers). 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.
Frizzil is collaborating with SMP to entirely retexture it. Expect something very, very awesome in the near future.