Dissidia's divided into stages, each taking place on its own checkerboard-like map.
You'll move your character around like a pawn, picking up equipment and potions on the map and fighting whenever you stop adjacent to an enemy pawn.
To move around on the map you'll need DP, or "Destiny Points".
You earn more DP by defeating non-boss enemies, and the more DP you have at the end of a stage, the more bonus stuff you'll get.
The boss of the stage is usually on the other side of the map, and what's worse, your energy isn't refilled after a battle, so grabbing items on the map is important.
A side note about the non-boss enemies, Duckroll from NeoGAF pointed out that they are Imitation versions of other characters. For example a screenshot in the latest scans show the Warrior of Light next to an enemy pawn that says lvl2 Imitation Kuja.