If the politicians had their way This Rule of Thirds would have an entirely different meaning
Take the money you make each month and divide it into three equal portions
The first portion is automatically seized by the Government
The second portion is consumed by your mortgage company or landlord
While the remaining portion, is shared by your spouse, your children and you.
I'm only Kidding
By dividing a picture into a grid with three vertical lines and three horizontal, it is typically most powerful when the focus of concentration is within the juncture of two of its perpendicular lines. This rule of thirds therefore is a rule of composition that's been around for centuries and famous artists have followed it over hundreds of years. This rule is actually about positioning your subject within the image. Actually it's not a rule at all, rather it's a guideline for creating practical framed photographs.
Rule of thirds with a cropped image on the right to conform to the rule
Adjust By Cropping Your Image
Cropping is simply cutting the image down, although not necessarily by size. It's quite possible to select a image such as this one on the above left and remove a portion of the "dead area" on it's left side. The resulting photo conforms to the rule of thirds with a resulting a stronger feeling.
Consequently this rule of thirds becomes an imagined tic-tac-toe template depicted across a picture, breaking it into nine evenly balanced squares. The strongest focal points being where the four points of these lines intersect. The next strongest focal points being the lines themselves.
To make use of this rule of thirds just pretend there's a grid superimposed on each scene as you frame them in your viewfinder. If your camera is autofocus, then use the points of autofocus as reference points to help you image the grid.
If you employ an LCD monitor to frame your scenes you can make up a grid for your rule of thirds from clear window cling material. Another option (you should avoid this one) is draw the grid upon your camera's viewfinder (however not lens) however this may prove difficult to remove.
With some practice you'll be able to virtually imagine the grid every time you shoot.
Advocates of the technique maintain that by aligning a scene within these points, more tension is created, giving more interest and energy to the composition than merely centering the subject. Points of attention in your image don't need to actually come into contact with one of the grid lines to benefit from the rule of thirds.
In Actual Use
Using any inflexible composition guidelines in general are frowned upon, as there are numerous circumstances in which you're better breaking them; the primary reason for abiding by the rule of thirds in the first place is to deter placement of a subject in the center, or stop a horizon from cutting the image in half.
When capturing photographs or filming people, it's quite common to align the body using a vertical line, while featuring the person's eyes parallel with a horizontal line. When filming a subject that's moving, an identical method is often used, with a major portion of the extra space being placed on the front side the person or in the direction they are moving.