There are two types of maps in Battalion: Arena, Battle Maps and Coop Maps.
On Battle Maps, players fight against each other. In order to win on a battle map, you have to defeat the other player. Battles may consist of 2-4 players, depending on the map.
On Coop Maps, players cooperate to defeat a common enemy. The enemy forces are computer controlled and use the same AI as when playing single player maps.
See here about how maps structures looks like.