With no other pieces on the board, the advantage of a Pawn is enough to win a game. Here the White King prevents the Black King from chasing the Pawn.
Fight for the Pawn
Although the image is titled 'fight for a Pawn', the fight is already over. The King Black has failed to stop the advance of the White Pawn.
The White King on e4 is blocking the Black King on e2. If it is Black's turn to move, the Black King can't advance toward the Pawn. The best it can do is move sideways. If it is White's turn to move, the White King isn't required to move because the Pawn can move instead. Even if the White King did not stand between its own Pawn and the enemy King, the Black King would be too far away to catch the Pawn.
In two moves the Pawn will reach the 8th rank and will be promoted a to a Queen. The new Queen is already waiting next to the Queening square.