Key squares
For a pawn that has not passed the middle of the board, the key squares are the three squares two ranks in front of it. If your king reaches one of them, the pawn promotes no matter what the defender does.
Opposition means the kings stand on the same file with one square between them, and the side not to move holds it. The side with the opposition forces the other king to step aside.
The spare tempo
The kings face each other on e4 and e6, and it is White to move, so Black has the opposition. White's answer is a spare tempo: e2-e3. Now Black must move, the black king has to give way, and White's king reaches a key square.
Compare the same position with the pawn already on e3. There is no spare tempo left, and with best defence the game is a draw. The tablebase confirms both results.
The king moves Kd4 and Kf4 also win, but the natural-looking retreat Kd3 lets the win slip to a draw.
Remember
- King in front of the pawn
- Take the opposition
- Use pawn moves as spare tempi
- Key squares two ranks ahead