The side with the pawn holds only if its king keeps the enemy king away from the pawn. Step between the kings ("shouldering") rather than pushing the pawn too early.
Black has king and pawn against a rook, and it is Black's move. The pawn is safe for now, but the white king on f5 wants to come to e4, d3 and e2 to win the pawn. Black's only resource is the king: it must stand in the way.