Kings on e5 and e7, one empty square between them, and it is Black to move. That single detail is worth a full point here.
Black has to move, and any move gives ground. 1…Kf7 2.Kd6 and the white king has slipped round to the queenside of him. 2…Kf6 3.e5+ Kf7 4.Kd7 and now the pawn is escorted all the way: 4…Kf8 5.e6 Kg7 6.e7 Kf7 7.e8=Q with check. White never gave the black king a chance to stand in front of the pawn.
Who has it
The side that does not have to move. In the diagram that is White, because the black king on e7 is the one who has to step off the file. It feels backwards the first time you hear it, and then it becomes the most useful sentence in endgame play.
Two kings can never stand next to each other, so with only e6 between them neither can advance, and whoever is on move has to break the stand-off and step to the side. The other king then walks forward past him. In the diagram it is Black’s turn, so White owns the position.
Count the squares to check. One empty square between the kings as on e5 and e7, or three, or five: an odd number means the side not on move has the opposition. Two or four and the side on move can take it by walking in.
Direct, distant and diagonal
Direct opposition is the one above, kings a knight’s jump apart on the same file or rank with one gap. Distant opposition is the same relationship stretched out, kings on e1 and e7 with five squares between. It converts: if you hold the distant opposition and the kings march at each other, you hold the direct opposition when they meet.
Diagonal opposition works too, for instance kings on c4 and e6. Beginners miss it constantly, because they only look along files. When you are trying to stop an enemy king from reaching a square, check the diagonals as well.
The same position, one tempo different
Give White the move instead, kings still on e5 and e7, and the win vanishes.
1.Kd5 Kd7 and Black is simply copying: whichever way White steps, the black king steps to face him. 2.e5 Ke7 3.e6 Ke8 is the key moment, and 3…Kd8 instead would lose to 4.Kd6. After 3…Ke8 White has nothing better than 4.Kd6 Kd8 5.e7+ Ke8 6.Ke6, which is stalemate. Same pieces, same squares, one tempo, and the result flips from 1-0 to a draw.
That is why endgame players will spend three moves shuffling a king to hand the move back to the opponent. Learn to count the squares between the kings, then take a run at some king and pawn endings; after that, the technique with heavy pieces on the king and queen mate uses the same idea of walking your king up to arm’s length.