Of course, like any rule, it should never be followed blindly, especially in art. Think of it more as a guide line than a rule (said in my best Captain Jack Sparrow voice)
What is the rule of thirds?
Look at the picture below. It is sectioned by a grid. When you are taking a picture you want to visualize this grid and try to place your subject near the lines, especially where the lines intersect. As you can see, my son Ronan is placed at one of the intersections. This is the rule of thirds.
When you are taking a photo, think about your composition and placing your subject near the line. It doesn't have to be perfectly on the line, just near it. This may mean that you have to move around to get the best angle, but thinking more about your shot is a good thing to do even when you are not using the rule of thirds.