Arena is the PvP (Player versus Player) feature of the game.You can gain honor, points that effect your ranking, and 5% - 10% of their current gold. This is not a good source of income due to having to pay a mushroom if you don't wait 10 minutes.
It is not recommended to type in someones name to fight or going to their page and press the attack button. Instead play what ever show up. This a good way if you should different weapon or equipment.