From the Super Mario Wiki
Battle Rings are small fighting arenas that Wario encountered during the events of Wario World. Upon entering a Battle Ring, which are always circular in design, a force-field would surround it, trapping Wario inside. Various enemies from the level would appear from nowhere and ambush the anti-hero. Wario had to use his various attacks to survive for 60 seconds.
Some Columns would always be inside the Battle Rings for Wario to use as weapons. After the 60 second time limit was up, a Wooden Chest would appear, containing some Coins. The more enemies Wario defeated in the sixty second time limit, the more Coins he would receive. Wario would then be allowed to continue on his journey through the level.