The fighting zones are for the bored shinobi and shinobi looking to have some creative fun that requires role-play.
The fighting zones are located in every village and all are connected (if you're in Otogakure, you could still fight someone in Kirigakure or any other village). In the fighting zones, there are 21 seperate zones, each having unique backgrounds for the landscape (note that half of the zones can't be reached until recieving a set amount of Orochimaru Kills).
Also in the fighting zones, are private zones. These zones are meant to be peaceful and away from the crowd so the two shinobi can get on with a battle. These zones cost gold (dependent on your level) and you may only fight one person at a time in these zones.
For more information on the zones, read How to Zone Fight.