If your king protects the pawn from "behind" they will together march to the other side of the board but there it ends in stalemate, not checkmate - if the opponent plays his king right.
Only if you get your king in front of the pawn and you have the king opposition - like at the end of your analysis - you can win the endgame.
There are many ins and outs to winning or drawing endgames with just one pawn, so you should make a study of them. One post is not enough to explain it all. And it is definitely worth the time to study endgames with more pawns as well. Though the pawn is a humble chess unit, there are many secrets to its proper handling.
Thanks for your answer, I thought that it was only possible for the opposite king to force mate, when the pawn is either on the a or h file.
So I know they explained it already but here are some pictures to help.
This is an example of zugzwang. Whoever moves first loses the game or their initiative.
In this position it doesn't matter who moves first white wins because their king is far enough ahead of their pawn. They can waste tempos with the pawn at will to put black into zugzwang.
If it's the a or h file you can win as long as you prevent the enemy King from getting to the promotion square otherwise it's a draw.
Here are two examples.
Of course anytime you add anything extra it gets way more complicated like this for instance.
If you're interested learning more, shoot me a dm and I'll offer some resources to help.
