Knight endings follow pawn-ending logic: an outside passed pawn drags the defending pieces away and the king penetrates on the other side. Knight checks gain the tempi needed to make it work.
Botvinnik observed that knight endings behave like pawn endings, and this position shows why. White has an outside passed pawn on a4; Black has a blocked f-pawn. In a pure pawn ending the a-pawn would decide, and here the same happens with a knight-powered twist.