The fork is the Knight's deadly weapon. In chess the fork is a double attack and it is a technique which the Knight is most adept at owing to it's unique move. The Knight can attack two pieces at once.
The opponent is forced to save the more powerful or maybe rather more important piece leaving the other hanging and this second hanging piece is captured.
If the King is one of the two pieces attacked in the fork, clearly he is the one that must be saved. That leaves the other one open for capture.
In the diagram, if 43.Ne5+is played, the Black King is in check and the Black Queen is also under attack. The King must move, the Queen is lost and there is nothing Black can do about it.