In chess, a smothered mate is a checkmate delivered by a knight in which the mated king is unable to move because he is surrounded (or smothered) by his own pieces.
The mate is usually seen in a corner of the board, since fewer pieces are needed to surround the king there. The most common form of smothered mate is seen in the adjacent diagram. The knight on f7 delivers mate to the king on h8 which is prevented from escaping the check by the rook on g8 and the pawns on g7 and h7. Similarly, White can be mated with the white king on h1 and the knight on f2. Analogous mates on a1 and a8 are rarer, because kingside castling is the more common as it safely places the king closer to the corner than it would have the castling occurred on the queenside.
For a smothered mate of this sort to occur in a game, it is usually necessary to sacrifice material to compel pieces to smother the king – a player is unlikely to voluntarily surround their king with pieces in a position where a smothered mate is possible. One method is particularly common and involves: check with the knight, then move the knight away to deliver a double check from the queen and knight, then sacrifice the queen to force the rook next to the king, then mate with the knight.
An example is to be found in the game between Jan Timman (White) and Nigel Short (Black) at the 1990 Tilburg tournament. From the diagrammed position, play continued 27.Nf7+ Kg8 28.Nh6++ Kh8 29.Qg8+ Rxg8 30.Nf7#. (Note that White would force mate even if his rook, and pawn on e7, were removed from the board, and Black had a knight on f6. In that case, 27.Nf7+ Kg8 28.Nh6++ Kh8 (28...Kf8 29.Qf7#) 29.Qg8+! Nxg8 (or 29...Rxg8) 30.Nf7 still mates.) This technique is so common as to have its own name: Philidor's Mate or Philidor's Legacy (after François-André Danican Philidor). This is something of a misnomer, however, as it is earlier described in Luis Ramirez Lucena's 1497 text on chess, Repetición de Amores e Arte de Axedrez, which predates Philidor by several hundred years.