The crooked path is useful when manoeuvring your king towards a pawn or an important square. Unlike straight-line movement, the crooked path allows your king to influence more squares and control the opponent’s king’s movement. For example, if your king takes a zigzag path towards a pawn, it can cut off the opposing king’s route, forcing them to waste moves and allowing your king to gain a crucial tempo. This technique is especially helpful in preventing your opponent from trapping your king or stopping your pawn from promoting.
Notice that all routes taken from e1 to e8 are 7 only moves each
In this first example White tries to capture the Black pawn by taking a straight line approach, but the Black King has time and saves the day with a draw.
This time the White King takes a 'crooked path' approach which blocks the Black King and forces it to take a side step resulting in the White King gaining a Tempo and going on to win.