Centralization is placing your pieces toward the middle of the board, where they control the most squares and can switch quickly to either wing.
A piece in the centre simply does more: a knight on d4 or e5 reaches far more squares than one on the rim, and a centralized queen or rook radiates power in every direction. The old maxim 'a knight on the rim is dim' is the flip side of the same idea.
Centralization matters most in the endgame, where the king transforms from a liability into a fighting piece. Marching the king to the centre — d4, e4, e5 — so it supports pawns and attacks enemy ones is often the single most important winning plan.
The principle competes with king safety in the middlegame: you centralize pieces, but you tuck the king away until the queens come off. Once the danger passes, bring the king out and into the action.
From the centre a knight reaches up to eight squares and can jump to either side of the board; on the rim it covers only a few. Central scope is what makes knights powerful.
In the endgame, once the queens and most pieces are off. The king becomes a strong attacker and defender, so marching it to the centre to support your pawns is often the key winning idea.
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