This green button is the "Search" function. It's for when you don't know where the enemies are. Pressing this button lets your character (Blockman) find the enemies by simply following the field until it reaches an enemy. This is useful in situations where there are pieces on top of pieces so you can't see them; or, when one piece is blocking another piece. The only drawback is that Blockman will still follow the same path (if possible) without stopping to wait for you to change his direction if something obstructs his way; but, I guess that's what makes it a "Search" function instead of an automated movement feature.