Pawn Endgames: Key Squares
Key squares are what we call those squares whose occupation by the king assures victory, regardless of whose turn it is to move.
The d5-square on which the king stands now is not a key square - White to move does not win. The key squares are c6, d6 and e6. Black to move must retreat his king, allowing the enemy king onto one of the key squares. With White to move, the position is drawn, since he cannot move to any key square.
With the pawn on the 5th rank (see diagram below), the key squares are not only a7,b7 and c7, but also the similar 6th-rank squares a6,b6 and c6. White wins even if he is to move.
Consider the next case, where the key squares are a6,b6 and c6. The sensible thing here is to head for the square furthest from the enemy king, since that will be the one hardest to defend.
Note: An analogy to help you remember the significance of Key squares - Think of a parent and a child crossing a road to reach school: A parent will always lead the child across the road rather than pushing the child in front. Similarly, the King (parent) should always act as a shield and lead the pawn (child) to the queening square (school).
Sources: Mark Dvorestky's Endgame Manual , Pawn Endgames
