This question is asked each time I explained the game for the first time to people. But after playing one game everybody understands why placing an additional object in your turn is so important.
First it helps to increase your (biggest) city by one.
Second it can block the route of your opponent(s). You can simply block their way to a important object (temple or statue), so they have to move around it. Or you can use it so block access to a mine (which is very important, because you need marble to expand).
So try the game out yourself and after your first game, you'll recognize the importance of squares.
That's kinda what I figured, they are there to place an additional piece for one action. Just didn't know if I missed something, I'm sure they have tactical importance that is better realized with experience