The town square is the center of all towns, and is required to start any city or town. The only item required to construct the town square is a single flag , even on a moonbase. They also require no labor to construct. If left by itself with no constructions being added around it for 72 real life hours, the town square will disappear. It will also disappear after the same time period if you delete all buildings in the town and leave it be.
If enemy troops enter your town square, they will start to take over the city (lowering your flag and raising theirs). In order for a town square to be captured, all defending bases must be captured first.