The arena is an island where you can battle other players and collect trophies by beating them. There are 3 tiers: bronze, silver and gold which can be unlocked once you earn enough trophies. There is also a friend tier where you can battle your friends via facebook.
Also, for every battle you enter you receive a statue chest which contains items to decorate a statue. These items provide a boost to you in battles increasing attack, defense or HP - the more you find the more you can upgrade the item and the better you will become in the arena. Your statue changes colour depending on your tier.