Unlocked when you complete Level 25, the Arena consists of Daily Tournaments. (so far, we might see special events/competitions down the line)
What I found interesting is the "endless mode" nature of the tournament. As opposed to playing multiple levels like Angry Birds Friends, you are playing a level with endless stages. So it encourages you to use your birds wisely, and maximize destruction. I wish Rovio could include the number of stages cleared next to the score.
You compete in a global leaderboard (not with Facebook Friends) organized in Leagues similar to Epic and AB Friends. But to move up the ladder, you need to level up your birds by collecting feathers.
I also wish they gave players the option to use a nickname to add an extra layer of privacy.
Post your questions/ideas below.