Key squares are specific squares on the board whose lasting occupation by the king (or another piece) guarantees the conversion of an endgame advantage, most commonly by ensuring a pawn's promotion.
In a king and pawn versus king endgame, each pawn has its own set of key squares — typically the squares located two ranks ahead of it, on its own file and the adjacent files. If the stronger side’s king manages to reach one of these squares, pawn promotion becomes inevitable regardless of the opponent’s defense. For instance, for a white pawn on e5, the key squares are d6, e6, and f6: landing on any of them with the white king secures the win.
In practice, the player with a passed pawn should immediately identify the corresponding key squares and direct the king toward them as a top priority. The defending side, in turn, must keep the king positioned to prevent that access — this is often the central battle of the entire endgame.