Rule of Thirds sample - Mommy's CameraCredit:

Rule of Thirds - The rule of thirds is a compositional rule of thumb in visual arts such as painting, photography and design.

Whether you are trying to put together a video shoot or stage a still photograph a key consideration is putting together a piece that is interesting and arrests the attention of your audience. This can be tricky when you are trying to translate a scene from real life to the screen or as an image. Something that is fascinating in real life may come across as boring. One way to keep the scene interesting is to put it a little off balance, the key to making something memorable is to present it in at least a slightly different way than your audience is used to experiencing it.

There are a number of different ways to accomplish this, one simple method is to use the Rule of Thirds. It is not a silver bullet for composing interesting, well frameds shots but, it can be a very useful tool.

As a somewhat novice videographer I have used the rule of thirds for some shots and found that it has helped me to give them good balance. However, as you get more comfortable with this rule you will definitely encounter instances when it makes sense to break it. If nothing else, keeping the rule of thirds in mind when I'm framing a shot helps me to keep focused on keeping my shots interesting and balancing them for easy consumption by my audience.

Basically, the idea is that you look at a shot and divide it equally into three parts both vertically and horizontally. You end up with a grid of nine cells or boxes.  You can use the intersecting points of the grid as a way to focus different parts of the shot, I've heard it said that you can use them sort of like cross-hairs. If you place the most interesting pieces of your image or shot at the intersecting points of the grid it helps to build a well framed shot. It is also supposed to allow you to  comfortably guide your audience towards what you want them to focus on.

You can also use the Rule of Thirds to change the distribution of the 'weight' or focus of your shots. For example, you could put the heaviest part of a shot in the right third of the frame, which establishes a feeling of importance for that portion. And, the audience is more interesting in viewing the shot than if it is centered because it is a somewhat unique view of your subject.

This image from Mommy's Camera is a decent example of before and after shots varied using the Rule of Thirds and it shows how moving the subject off-center can make an image or framed shot appear more interesting.

You'll get the most from this idea by just playing with it and seeing what works for you and your style. But, I think that simply being that much more aware of your framing will improve the quality of your shots a great deal.