Dungeons are thematic mazes that have unique enemies and bosses, and are found in the Dominion. While most dungeons simply need to be rushed, there are some that have mechanics and puzzles. For instance, in the Shrine of Devas you need to destroy each corresponding Idol to activate each boss. Endgame dungeons provide the player a way to get Health and Mana gems.
Beginner dungeons are meant to introduce players to the game. They are easy dungeons to complete on any character. The Primal Marsh will give you the hardest time if you're trying to rush.
Once you're able to successfully complete the Beginner dungeons, you might start thinking about Intermediate dungeons. These dungeons will throw different status effects at you and reward you with much greater loot.
Endgame dungeons will challenge even the best players in the game. In a large group, these dungeons are a breeze, but in smaller groups these dungeons are dangerous even to a maxed player. It is not recommended to do these dungeons unless you have a solid understanding of the games' mechanics and can at the very least dodge.