The concept of key squares, in general, is defined for pawn endgames with immobile pawns. It defines a winning strategy in two steps.
- Occupy one of the key squares with your king (usually, using zugzwang).
- Once this has been done, the opposing king cannot defend his pawns passively (but you should computre whether it can counterattack).
A typical example is the theory of the endgame King+pawn vs King. The result of any position with this material can easily be determined using the key squares, as explained in: http://chess.stackexchange.com/a/9239/9082https://chess.stackexchange.com/a/9239/9082 .
Your example is about opposition, and thinking in the terms of key squares doesn't seem to really clarify things here. In general, an opposition should be linked to a certain "axis", and here the plan is to use the 7th row. Here is what happens if White tries to use the opposition with the 6th row as an axis:
[FEN "8/5k2/1K4p1/5p1p/5P1P/6P1/8/8 w - - 0 1"]
1. Kb7! Ke6 2. Kc6! Ke7 3. Kd5? Kd7 4.Ke5 Ke7 {and Black holds the opposition, while the white king has not reached the key squares. Draw}
The correct plan is this one:
[FEN "8/5k2/1K4p1/5p1p/5P1P/6P1/8/8 w - - 0 1"]
1. Kb7! Ke6 2. Kc6! Ke7 3. Kc7!? Ke6 4. Kd8 Kd5 {The tentative of a counter-attack comes too late} 5. Ke7 Ke4 6. Kf6 Kf3 7. Kxg6 Kg4 8. Kf6 Kxg3 9.Kg5 {White wins}
You can find similar examples the book of Mark Dvoretsky "Endgame Manual".