The Mysterious Portal teleports you to a Strange Dimension. It is a tile charged with blue magical energy.
Oh, you want to know what a Strange Dimension is? Well aren't you needy.
A Strange Dimension is a separate, special floor of the dungeon that can only be accessed by a Mysterious Portal. According to the minimap, it says it is Level 0.
The most notable feature of this floor is that it is populated by a small number of completely random enemies from throughout the dungeon. This makes it an extremely dangerous place for lower-levelled characters. Also note that as the floor counts as Level 0, all monsters' base stats are scaled accordingly - an Archdiggle found here is easier to defeat than one found on Level 10, but still very deadly.
The visual design of the floor is copied from a random floor in the dungeon. Rather than a mash of connected rooms like the regular floors, this floor is smaller and every room in this floor (except the start and end rooms) only have two doors, making a one-way path from the starting point to the exit point (another Mysterious Portal that teleports you back to where you came in). Additionally, the floor is populated by a small number of completely random enemies from throughout the dungeon.
Items and Dredmor statues do not appear normally, but chests do. These (slightly rare) chests also contain items of random rarity, making portals appealing for early characters to potentially get late-game loot, if they're sure they can survive. Other than that there are no special items in the Strange Dimension, and no reward for passing it.
Completing the Strange Dimension will earn the achievement "The Magic of the Wizard's Hangover" if the player has not previously completed a Wizardland.