The human eye has a natural tendency to be drawn more strongly to certain parts of an image. So, imagine a tic-tac-toe board drawn across your photo to break it into nine equal squares.The four areas where the tic-tac-toe lines intersect are the strongest focal points. Then, the actual lines are the next best focal points.
So, if you try to place the part of your image that you want people to notice into one of these intersections or lines, your photo will have more oompf.
Here are a few examples, but please note that I am not a complete rule-follower!
By placing Ella in the top right part of this picture, the eye is naturally drawn to her, while creating interest by showing the arc of the tree and the curve of the bridge, as well as more depth.
If I had just put her in the center of the frame, the picture would have lost some of that interesting detail.
With this picture, one of the grid intersections would be near her left eye. Again, this makes the picture more interesting and it shows her natural surroundings.
When I take photos of people walking on paths, I like to try to put them in the bottom of the grid or the top of the grid. It is much more visually appealing than placing them smack-dab in the center.
The Rule of Thirds is something fun to try, especially if you feel that your photos need that extra boost of interest. It does not work for every circumstance or every photo, so don't feel limited by it!! Just give it a shot!