Triangulation looks often rather unnatural. To understand it, you need a good feeling for concepts like Zugzwang.
In the diagram *) to the right it is White to move. If White would be allowed to skip his turn, he would do so. He would stay with his king on f2 forever making it for Black impossible to play Kg3 followed by the promotion of the f- or h-pawn. If White had the choice between moving or not, he wouldn't move. And in that case Black had no possibility to win.
But White has no choice. He must move, even if he has only loosing moves at his disposal. So in the diagram White is in Zugzwang.
Now let us go a little bit back.
In the next diagram it is White to move and it is an easy win for Black.
Now let us look to the same position with Black to move. How should he play?
In the last diagram Black essentially made a triangle with his king and reached the exact same position where he started except this time it is his opponents turn to move, that is: the 2nd diagram.
By the way, did you notice that the last 3 diagrams would be a clear draw without pawns on h3 and h4?
The next example comes from on TheChessWebsite.com. There you will find a explenation on YouTube. First let us look what happens if Black is to move. Well, actually that isn't exciting because than it is an easy win for White.
Now let us look at the same position but now with White to move. That is more exciting. Actually White spoils a whole point if he plays the most normal looking move:
White wins if he plays it a little bit more sophisticated and uses triangulation.
White should play with his king the triangle d2-e2-e3. That is loosing a tempo (The White pawns on c4 and f5 Black playing the same manoeuvreor). One can also say: White won or created a spare tempo, White is on the right time on the right place!
This first 3 diagrams come from: