I'd imagine it's because from the center, you can span a larger area than from edges or corners. From the center, you can reach all the corners of the board, including where your opponent's king is, so you can attack it.
And the knight benefits the most from it, because percentagewise, it increases its span much more compared to the other pieces. The rook probably benefits the least, since its span is constant, and with a crammed board, a centralized rook can become a cumbersome liability.
The pawn benefits least since pawns always attack two squares unless they are rook pawns, a pawn doesn't suddenty have influence over more squares just because it is closer to the center of the board.
i don't usually pay attention to centralizing units during the entire game, my mind's on mobilization of all units and then look for weaknesses, either on the flanks or diagonals. I'm not like "hey, i've finally placed a knight on the center which is logically strong..." Pieces only become strong when placed on vital squares that are part of a combo attack. IMO.
The knight benefits most and the rook the least. I am old school I guess that I dont consider pawns as "pieces" but for arguments sake lets say they are. The a and h pawns attack only one square while their more centralized cousins all attack 2 . On an empty chess board a rook hits 14 squares no matter where you place it.
knights benefit most and its important because their king is on the other side so if your pieces are in the center you are closer to checkmate
The number of squares may be the same but a rook on the center of the board hits 4 different directions at once while a corner rook is only going in 2. But the pawns are always moving in one direction, regardless of their location on the board.
The rook benefits least and the knight most from centralization, this is easy to verify for yourself on an empty chess board.
In the end of the middle game or end game with Queens, centralisation of the Queen is very powerfull way of playing imo. About knights i rather have a knight on the 3e rank(enemy side) then right in the center.
Rooks in the centre can be quite powerful: http://www.chessgames.com/perl/chessgame?gid=1441056
who says computers cant be creative?
Apart from the fact that most pieces control more squares when placed in the centre there's often also one another important benefit from centralization: since the distance to different squares on the board is on average shortest from centre a centralized piece can be faster moved to a new post than one on the edge. I believe this is the principal reason why centralizing the king (the slowest piece) is so powerfull procedure in an ending. Obviously long range pieces don't benefit as much from this as a knight or a king would.
Why is it important in chess ? Do you know which chess piece benefits most from it and which benifits the least ?