Center control is an important aspect of playing chess, most openings are built around controlling the center, but why? Is center control really that important for winning a game?
The center is the crossroads of the board. Controlling it will give you access to every other part of the board. At the same time, it will drive a wedge in the opponent's position that hampers communication between king and queen side.
Control of the center is usually a decisive advantage in your favor; unless your opponent has heavy compensation (e.g. more than a pawn of material advantage), or a violent attack against your king.
First of all, EVERY reasonable chess opening is focused on the center in the first few moves. Even hypermodern are focused on the center even if they don't play for it directly.
Why is it important?
White has the first move advantage and there are a finite number of squares on the board. If white can turn his first move advantage into controlling more squares than the opponent then white can have a sustainable advantage. Otherwise, white's advantage will dissipate into nothing as the game goes on.
You could say why doesn't white grab space on the wing? The reason is that the opponent can grab more on the other side. If you play 1.g4 and I respond with 1...d5 I'm at least equal because I control more of the board.
Another way to look at it is this. Whenever you put a game into an engine it gives you a score. That score is based on the value of the pieces. The value of the pieces is based on their mobility and their mobility is based on control of space specifically in the center.