"Mario Levels" are sub-zones (like Instances) which are dedicated to testing the players agility.
This is an example of the Asura Jumping Level:
As you can see, it's very arcade-game like, with dodging environmental challenges (like wind and lightning), combined with skill-based actions (like accurate jumping!) and some complete arse things (like having to attune yourself to portals before entering, otherwise you just get ported back to the beginning!)
Apparently, there is one of these in each starting zone.