You do not earn exp when competing in arenas, chiefly because you must die to exit and gain your prize.
There are currently 3 arenas in Battleheart:
The Haggerdom Arena
The Haggerdom Arena provides low tier armor, weapons and trinkets. All of these items can be obtained also by upgrading/purchasing from the shop, which makes this arena mostly useless and a waste of time, unless you have a burning desire to not level up and obtain your low tier armor without spending a relatively large amount of gold.
The Brightstone Arena
The Brightstone Arena is the second arena encountered in the game, and as such, it drops moderate tier items for the most part. However: if you kill 115+ enemies in this arena, you earn Tier 8 items. If you kill 140+ enemies, you can earn Tier 9 items, which CANNOT be obtained outside of Arenas. This arena is useful, however it is not advisable if you've unlocked the final arena, seeing that the Doomvale arena is less time consuming to earn equal and better rewards (despite the fact that it does require higher level characters and better armor to complete)
The Doomvale Arena
The Doomvale Arena is by far the best of the three arenas. It drops Tier 7 and below until you reach 50+ kills, at which point it drops Tier 8 items. If you reach 70+ kills, it will drop Tier 9 items, which are the best items in the game!
Tip: Tanks are actually very useful in this arena, and good healing is vital. This is mostly due to the red slimes, which, even at medium killcounts (30-40s), can do pretty heavy damage. They also relatively frequently appear in groups of 2 or 3, which can make them extremely dangerous to anything but a heavily armored tank-role character (EVEN WITH VERY GOOD ARMOR LIKE TIER 9, THEY CAN STILL DO HEAVY DAMAGE). The best way to deal with this is to focus all attacks on one slime until its down, and then move to the next, and so on.
If you are having a hard time dealing with red slime you can use a Knight's 'shield wall', because it reflects 100% damage back at an attacking enemy, and so red slimes deal a huge damage back to themselves. However, you should be wary to know when your shield wall runs out, as being bitten by three red slimes at the same time can be deadly.
Tier 8 items can be obtained from the last boss in Doomvale and arenas and tier 9 items cannot be obtained outside of arenas. There are Tier 8 weapons, however there is no Tier 8 Armor. Tier 9 includes both weapons and armor, however neither Tier 8 nor Tier 9 feature trinkets.
Another great use for arenas is the ability to detach armor from a unit and send it into the arena alone. This will give you the lowest loot from each arena, but is free loot that can be sold for gold.
IMPORTANT: If you reach a kill 'point', for example: in the Doomvale arena, if you kill 70+ enemies, you will ALWAYS receive a piece of Tier 9 loot. Likewise, if you kill 50+, you will always earn a piece of Tier 8 Loot, and nothing lower. The difficulty increases as your kill count rises, so it is advisable to be well levelled and maxed in Tier 7 before you begin trying for Tiers 8 and 9.