Depending on the quest choice, the game engine will create a different maps for the adventure. The map will vary in size and theme. They may also have map specific cards and events which require your character to explore multiple maps/dungeon levels to complete.
Dungeon level tells the player how advanced in the quest their characters is at any point in time.
Dungeon level is also used to calculate chances of finding enchanted and unique equipment as well as affects the enemy experience level encountered by the player. To advance the dungeon level use an exit card, generated somewhere on the map. The card will have a unique name and will immediately open new map upon interaction - please note, once used, your character may not be able to go back to the previously explored areas.