You must have use your king in the endgame that is what you have read somewhere from the book, heard from your coaches. But have you ever noticed that it is much easies for you to use your king in the endgame when facing weaker less experienced players? Why is this?
In my view the following factors play an important and decisive role here:
1) More active & mobile pieces: When you have more active pieces you can often restrict the activity of your opponent’s king. For instance if you have a rook on the 7th rank it can tie the opponent’s king to the 8th rank.
2) Pawn weaknesses or pawn structure.
3) Piece coordination.
First point is very easy to explain but other two are more subtle. I think they are illustrated by two games from the World Chess Championship played between Petrosian and Botvinnik in 1963. In both the games, Petrosian had the better king than Botvinnik. I strongly recommended readers to study both the games bearing in mind the points above.