What is the rule of thirds? Its a way to teach photographers how to line up their subject to create a more balanced image. When you have a grid to work with, the subject of your image would be placed on one of the lines or at a cross section. The center of focus should be where the lines cross.
The idea behind this is that placing points of interest in those cross sections the photo is more balanced and easier to look at. When looking at photos, your eye will naturally go to one of the cross section, using the rule of thirds works with this natural way of viewing a photo rather than against it.