The rule of thirds helps you position your frame. Imaginary lines divide your viewfinder or screen into sections, like this:

The rule of thirds helps you with composition and mood. For example.. if you're taking a picture of a person, you don't want their face to be directly in the middle of the shot. Move your camera a tiny bit over, so you can capture everything you want to without the person's face being the thing that divides the photo in half.
If you are shooting an action, make sure you get the full move in your shot. You want to let the viewer know what is going on instead of leaving them with a head full of questions.
Example:

The photo on the left shows the soccer player running by, while the one on the right shows her getting ready to kick the ball and make a play.
Sometimes it okay to break the rule of thirds. You can break it if your subject is too large to fit nicely in one of the intersection points, if centering the image would help to show a certain concept or if you want to show symmetry.
You can also use the imaginary lines to show depth and draw people into your photo. Try not to leave them wondering about what is going on.
That's the best way I can explain it, let me know if you still have questions

I took the photos from random sites, I can post better images if you'd like.
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blind.
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