I don't really understand the map.. :(
Each square is a city block.
The numbers and letters on the left side and top act like one of those fancy graphs, eg "B 11" would be
here (purple block being the selected one).
When you choose a square to operate on, it will recieve a slightly smaller square inside it with the operation's color, keeping a small outline so you don't forget what it's original color was.
Eventually the attack will be complete once a decent amount of enemy squares are filled in.
Hope that helps.