In this photo, notice how the main focus, myself and the mountain, are in the top two corners of the photo. The extra space fills the center. Since the main two focuses are in the corner and not the center, this allows the readers to draw there attention to these main objects and not the center.
In this photo, the main attention is on the birds. When we use the rule of thirds, we are able to notice that the birds is in the top left corner of the picture. This is important because the viewers attention immediatly draws to the birds rather than the extra space.
This photo is of a statue in plaza mayor in Madrid. Notice how the top of the statue is in the top left corner of the grid. This draws the viewers attention to the statue rather than the extra free space in the background.
This photo is from Park Guell in Barcelona, Spain. When taking this photo, I purposefully wanted the tower to be in the upper right hand corner. This attract the viewers attention due to the law of thirds. This statue also stands out by having the background be a bright blue, which contrasts the white statue. In the middle of the photograph, there is empty space, this again helps draw viewers attention to the statue rather than the houses or sea.