In downWorld there are many locations. Most of which you fight in. The locations that you fight in are divided up in small arenas (each including an enemy).
After you kill the enemy in one of the arenas you can move on to the next and you can backtrack either by clicking the exit door or clicking the squares that are lit up in your arena map. When you go back, though there will be no enemy. In order to reload the entire location you must defeat the enemies in all of the arenas. After killing all the enemies the next time you come back the location will be reset and you will have to start back over from the being.
Some of the challenges require you to do this in order to retrieve something.