The Monster Arena is a building from which players used to engage in PvP multiplayer battles. That game mechanic is now incorporated into the gameplay, apart from the building. By default, players have a maximum of 2 multiplayer attack points. Building the Monster Arena increases that to 3.
The building is available to purchase when multiplayer becomes available, at player level 10. It is officially categorized a decoration. It is a 6x6 unit building that sells for 12,500.