A king and pawn ending can be hugely complicated precisely because it is possible to calculate long variations. When there are lots of pieces on the board you have to rely on general principles rather than exact calculation- and that can make it easier, even if you dont actually make the correct choice of move then you may not get punished immediately.
Two kings cant move next to each other, therefore there is an invisible barrier created when two kings are separated by the distance of one square, either diagonally or directly face to face. When two kings are opposing each other the player not to move is said to have the oppositon.
Black can have 2 main moves that is Kd6 or Kf6, in either case it is impossible to prevent white king from occupying either Kd5 or Kf5, after which black will lose a pawn and the game.
But imagine if it was white's move to play, then black has the opposition but unlike white black can only draw even with the opposition advantage. As here black king is behind the pawns unlike white king when it had opposition.
Lets look at another example to understand the importance of Opposition
This is a very critical position,here whosever turn its move loses the game as opponents will get opposition and pawn cant be protected.
The value of opposition in the pawn endgames is immense, and very often decide the outcome of the game.