All the squares on a chessboard are not created equal, any more than any of the various types of highways are. To begin with, half of them are light and half of them are dark. Of course there is no essential difference between the dark and light squares.
The real difference between the various squares comes with their neighbors. How many squares does a particular square have bordering it? That's what makes some squares more equal than others.
Lots of Neighbors
Those squares that have many bordering squares are in the middle of a metropolis. There are pieces to see, squares to go to, and activity can be expected to be high. This is simply because there are many different directions that radiate out from such squares.
The geometrical center of the board (e4, d4, e5, d5) is where the most traffic will take place. The “greater center” of squares, encompassing c3-c6-f6-f3 and back to c3 and the center squares, usually encounters the next busiest activity. This is because these squares lead directly and quickly to anywhere.
For example, take a look at e4. There is the fourth rank, the e-file, and the b1-h7 and h1-a8 diagonals. In addition, the rectangular corners available from e4 are f6, g5, g3, f2, d2, c3, c5, and d6. Count up all the squares on major highways directly available from e4 and you will come up with an astounding thirty-five squares, or more than half the chessboard!
The Edge of the Board
On the other hand, take a look at the edge of the board. Anywhere along the a-file, the h-file, or the first or eighth rank will do. These squares all have some neighbors, but not nearly as many as those in our booming metropolis.
Let's do the same exercise with a corner square a1 that we did with the central square e4. From a1, we are directly connected with the a-file, the first rank, the a1-h8 diagonal, and the rectangular corners b3 and c2. That adds up to a paltry total of twenty-three.
Is it any wonder that one of the most important strategic principles in chess is to control the central squares?