Key Squares

So basically i have come across a topic on corresponding squares in an endgame book of mine and there is a position where the key squares are beside the pawn and one directly in front. My understanding of key squares in respect to king and pawn endgames is the general group of 3 squares 2 ranks in front of the pawn or the 6 key squares in front if the pawn has reached the 5th rank but ive never seen anything anywhere explaining how key squares can be next to a pawn. Im familiar with the Critical squares of a set of locked pawns but this isnt 3 squares extending out 3 files to the left or right this is like a cluster of seemingly random squares that are called key squares. after identifying these key squares you can then identify the corresponding squares. I need to understand how to figure out these special key squares before i can understand how to identify these corresponding squares.

https://chessprogramming.wikispaces.com/Corresponding+Squares