Everything about this ending comes down to one awkward fact: your bishop only sees half the board, so only two of the four corners are any use to you.
The king in that picture is perfectly safe. He is not safe because White is playing badly, he is safe because a8 is a light square and White’s bishop lives on dark ones. To win, White has to walk him all the way to a1 or h8, which is where the work is, and why this mate has a reputation.
The barrier, then the long walk
The method has three pieces doing three jobs, and they never swap. The bishop cuts a diagonal the king cannot cross. Your own king stands opposite his and pushes. The knight fills the single hole the bishop leaves, which is the one square of the wrong colour next to the king.
First you confine him to a rectangle, usually against an edge. Then, if he has picked the wrong corner (and a defender who knows anything will), you walk him along the edge to the right one, keeping the barrier intact the whole way.
That walk is the W-manoeuvre, and the name is literal. With a light-squared bishop the mating corners are a8 and h1, so the king is escorted along the eighth rank from h8 towards a8 while the knight hops f7, e5, d7, c5, b7. Plot those five squares on a board and you have drawn a W. With a dark-squared bishop the same route is mirrored, towards h8 or a1. The knight takes the escape square, the king steps up, the bishop holds the line, and Black shuffles one file closer to the corner he did not want.
What the mate looks like
Count the jobs again in the final position. The white king on g6 holds g7 and h7. The knight on e7 holds g8. The bishop on e5 gives the check into h8. Remove any one of the three and Black walks out.
Up to thirty-three moves are needed from the worst starting position, which is uncomfortably close to the fifty-move limit, so this is one ending where the fumbling around does cost you the point.
My honest advice: leave it. Get king and rook and two bishops fully automatic first, because those come up. Then, one evening when you feel like it, set up bishop, knight and two kings, and give yourself twenty minutes against an engine. It is the one mate that repays being learned slowly, and the knight footwork you pick up doing it shows up again in every knight endgame you ever play.