You can encounter Portals leading to special Dungeon dimensions during a Run.   

Going through the Portal will present you with a Dungeon Quest.

When you successfully complete the Dungeon Quest, you will enter the Treasure Chamber, where you will be rewarded for completing the Dungeon Quest with the unique Chest.  

In case you fail to complete the Dungeon Quest, don't worry, you will simply return to the regular Run straight away without receiving any reward.