Entrances to the Arena can be found in most (all?) major cities.
The Arena is where you challange 'ghosts' of other players to fight duels - gaining or loosing honor and rank based upon the outcome. You gain some honor for challanging another player and either gain or loose more honor and rank depending upon whether you win or loose.
Why do it? Well, other than for kicks, you can trade honor for gems to enchant items, runes to embed in items, experience points or gold. This appears to be the only way to 'purchase' gems or runes without spending dragon gold.
You are limited to a total of 20 challanges a day and there is a 5 minute cool down period between challanges.
Once you have challanged a player, the battle is fought out immedietly against a copy of the player that you challanged. Both yourself and the challanged player will receive a copy of the combat log in the mail.
There are a number of skills that affect arena combat and it appears that soul empowered items also give an advantage.