To draw or bring to a center point; to gather into or about a center; to bring into one system, or under one control.

The central placing of pieces and pawns so they both control the center and extend their influence over other areas of the board. A piece will usually reach maximum maneuverability and power when centrally placed.

To place pieces and pawns so they attack the center.

make central; "The Russian government centralized the distribution of food"