Take any image and divide it into thirds horizontally, and vertically. In images to which the rule of thirds was applied, the subject appears at the intersection of any of the thirds in the upper or lower right- or left-hand corners to create a visually interesting composition.

This picture ends up relatively boring when the flower is placed right in the middle of the image.

As you can see, when we divide this image into thirds and place the flower on the intersection of the farthest left and top third, the image is much more dynamic.