The bulk of the storyline for Meiyaku no Tobira takes place in various dungeons, as the title implies. Each dungeon is unlocked after various quests are completed by acquiring "plates" and can be leveled up by inserting jewels in said plates. Each level is more challenging than the previous one and can be selected at any given time. At one point Dungeon level progression is stopped until an item called a Sirius Jewel is acquired, a reusable item that unlocks further dungeon empowerment. Specific levels have specific challenges in them, such as Level 6 of a dungeon are considered blind; without the usage of a specific item, the mini-map is blanked out with only the character icons visible.
Source: Wikipedia, "Dungeon Explorer: Warriors of Ancient Arts", available under the CC-BY-SA License.