The arena is a place where you can fight other opponents. To start a fight, you need to choose one opponent out of 3 available. Depending on the result of the duel, you gain or lose honor and gold, as well as bonus XP for the first 10 victories of the day.
You can also attack by going to the hall of fame, but you won't get bonus XP then.
You can fight on the arena once per 10 minutes, however, you can use or watch an ad to fight again without waiting. Watching ads to fight on arena is limited to mobile versions of the game, and daily limit is 50.