Dimensions in Soda Dungeon are part of the progression of the game.
Once you have defeated the boss of a dimension, the first being on level 100, the second one being on level 200, the third one being on level 300... you will gain access to the portal outside of your tavern. This comes with a number of effects, it acts as a sort of 'soft' restart, removing your current equipment, dungeon levels, gold, and sodas. Other upgrades in the tavern and VIP areas should remain unaffected (except Fury X-treme and Smiley cola, it will be reset upon travelling to another dimension) , and essence will not be reset.
When you travel to the next dimension you will be given a choice of 'Relic' sodas, as well as a pre-determined relic that boosts the stats and abilities of a particular hero type permanently.
By progressing through dimensions the story line is progressed, with a new boss unlocked for each dimension.
There are 10 different bosses. Then you'll reach the final dimension, called Smiley dimension (SD). From that point on levels will still increment in dungeon exploration, but cycle through the same bosses.
The Lair of Despair is first available in the Dimension 2, and can be accessed by talking to Fabulo, who flies in a yellow jacket while fanning himself above the portal gate.