The Rule of Thirds says that when you divide the image horizontally by thirds
and vertically by thirds
you should place elements on or near the lines or intersecting points.
For example, if you have a horizon line, it should be placed on or around one of the lines located at a third of the image.
I made a quick example of a cliché sunset to demonstrate the use of the lower horizontal line:
Another quick image of a Martial landscape:
The Alice image in the previous section is also a good example of the Rule of Thirds: