Major pieces in chess refer to the queen and the rook, as opposed to the minor pieces — the bishop and the knight. They are distinguished from minor pieces by their raw power: a rook is conventionally worth approximately 5 pawns, and the queen around 9.
The defining characteristic of a major piece is its ability to control an entire rank or file on its own, and to deliver checkmate assisted only by the friendly king — without requiring any other piece. A king and rook are sufficient to mate a lone king; so are a king and queen. A lone bishop or knight, by contrast, cannot force checkmate without additional support.
In practice, major pieces reach their full potential in the endgame and in open middlegames. A rook placed on an open file exerts immediate pressure along the entire line and can single-handedly decide a game. The queen, too exposed in the opening, becomes formidable once the opponent’s minor pieces have been exchanged off. Knowing exactly when to activate your major pieces is one of the key skills to develop between 800 and 1400 ELO.