The rule of thirds describes a basic compositional structure of a photography. Taking any image, you can split it into 9 segments by using 3 vertical and 3 horizontal lines. The rule of thirds involves splitting an image up into 9 segments.
When looking at portraits you can see that the eyes will line up with the upper horizontal line and in close ups will go inline with the adjacent vertical line. When looking at landscapes The image should rest on the upper and lower horizonal lines as this adds more depth to the image making it more aesthetically pleasing.