Underpass, opposition and critical squares...

      In this final position, White's King heads to a3 and gains ground on Black's King.
Black manages to stop the White King from occupying the outside critical square--a5 by playing 3...Kb6, but with 4.Kb4 White takes Direct opposition, reaching a critical square c5 on the next move...and the rest, as they say; is a matter of technique.