The easiest way to explain things is that an image is made up of nine equal parts (refer to the above example). The "thought" or "rule of thumb" is that when taking a photograph, the point of focus should be placed along these lines or match up to one of the intersections. When taking a picture, most people probably never think about this concept. It's something I never used to think about. I just took pictures and aimed my focal points where my “eye” was directing me. I never thought that what I saw as a good shot, was actually falling in line with the rule of thirds. I always feel visual examples are the most helpful. Bellow are some pictures with the graph so you can see how the focal points in each image line up. If you've never heard of this concept, keep it in mind the next time you are out shooting and experiment a little. I would love to hear feedback on the effect it has on your images when applying it to your photography!
Happy Sunday!