This tutorial is more of one related to composition than to a specific technique. This was programmed into my head as an art student and I am glad that my professor took the time to explain it. Many creations are be general definition, wonderful, yet they suffer because of poor composition. It is not always necessary to center-align your image/focal point.
The Rule of the Thirds is an easily applicable rule of composition. Basically, your image is divided up by four lines as outlined below:

In terms of "good" composition, utilizing the "Thirds" means your image will hit at least 3 of the 4 points. I have two examples below of what this means, exactly:


Using the examples above, your image should "hit" the red circles, indicating the thirds. What this does is retain the viewer's attention to your image. You do not want your viewer looking at your work for 3 seconds and then looking at something else. After investing time and effort in your work, you would like others to truly look at it.
Utilizing the 3rds keep the eye rotating in the page. Obviously if you place arrows point outwards the viewer's eye will follow them. Hitting all four points, depending on the piece, can be "too much" for viewers often times.
For a practical example, here is a photograph that I took. This was taken at the University of Georgia, North Campus, in Athens, Georgia:
Yea, a chair... Chairs are rarely images that excite the mind, however, by taking a simple object and repositioning it within your composition, you make the final image more interesting to look at. If the chair here was centered, it would not have the same effect as it does being off to the side.
This does not apply to all images. In certain cases it is a good idea to center an image as that will be the main focal point of the work. In that case, centering would be the best solution. Keep this in mind when creating your work, and my art professor would be most pleased!