During the main game, the battlefileds are a separate area you reach by finding a BF key. They consist of a 5 traders, and several 3 level dungeons (3 in act 3, 6 in acts 2-4). Higher level BF keys will open additional dungeons.
The BF dungeons are randomly generated the first time you enter each act (the option appears on the secondary skill list by the characters' portraits after you have found a key in each act). Monsters do not respawn.
As LiraLindriel explained, the after game BF allow you to endlessly generate new BFs.