The idea is to place the key elements of your scene where the lines intersect as shown. This should engage the viewers attention and provide a natural focal point. For instance, in a portrait, keeping the eyes in line with the top intersection and the mouth with the bottom.
As for landscape photography, placing horizons along the horizontal lines and cliffs etc. along the vertical line will result in a much more balanced image.
However, like every rule it's meant to be broken, so it won't work for all scenes and situations. The fun is in finding out!
