Explanation

Queen and rook form a 3x3 box that traps and checkmates the king, giving the pattern its name.

Examples

White can deliver kill box mate with Rf8#. On the edge of the board, queen and rook already cover all the escape squares.

White can deliver kill box mate with Rd5#. The escape square e4 is blocked by the pawn. The queen also isn't guarding f4, but the pawn on g3 helps out.

Related patterns

In triangle mate, the queen delivers checkmate, and is protected by the rook.
In lawnmower mate, two major pieces deliver checkmate on the edge of the board.