For the same reason that we don't want a knight on the edge of the board, generally speaking - it can only attack / guard 2-4 squares instead of 8, so its power is reduced. And at the edge of the board it guards less valuable squares.
Likewise, to traverse the board from one end to another a piece must pass through the center. If it can't pass through the center, it can't traverse the board quickly... so it can't be used in as many combinations, its power is reduced.
Imagine you have a bishop locked behind a pawn chain, unable to get into the game... that bishop may as well be dead for how it effects the game, it's the same issue. Of course you might be able to free it in time, so how dead it really is depends on how much time you have - maybe it'd only take 1 pawn move to free your bishop, but you don't have time for that since you're trading or being checkmated currently. But maybe you do have time to free it, or time to move your pawn off the edge of the board... maybe it's not a problem (if you can justify the wasted time). So there is also this idea of ceding the center temporarily, but chipping away at it over time, that's a hypermodern idea.
And in the center you also threaten important central squares with your pawns, preventing your opponent from occupying them.
From the center you can also move in any needed direction, the center position allows for versatility. The options you do have are also more valuable, since they involve squares and pieces that are also more centralized... ultimately the center just has a gravity about it. LIkewise when deny your opponent options you are strangling him.
But these are generalizations, and chess is a very concrete mathematical game, so it doesn't always apply.
For example, if important play is happening on the side of the board, like your kingside is under attack and there are forcing combinations, then that becomes the most critical area and you can ignore the center to some degree.
Perhaps the center is more about positional play and the potential that pieces have, but when variations get concrete... the priorities can shift.
In general you can think of positional play as limiting the potential of your opponent while maximizing your potential, and you can achieve this by controlling space / limiting their space... controlling more space is often referred to as having a space advantage.
When calculation begins that's when potential breaks down into something actual, what matters at that point is finding a forcing combination of moves.
You could also say that forcing moves are the culmination of positional advantages, ...
That gets into the idea of threats - you also threaten more from the center... and threats tie your opponent down, force him into certain positions to defend.
Ultimately your opponent being tied down / limited in options, while you having alot of options / many threats, culminates in some forcing lethal combination.
As you can see the entire game is a struggle for control of space, in a way.
The center is important. Take a look and answer the title.