There’s a reason it’s called the “Rule of Thirds” and not the “Suggestion of Thirds” or the “Very Highly Recommended Concept of Thirds”.
Still, for the most part, photographers don’t like rules. More to the point they like flouting them with reckless abandon. Photographers are frequently the people climbing on street lights to try and get a better angle on the crowds, the ones hauling a ton of gear out into the wilderness at zero dark-thirty to catch that one moment of fabulous lighting, the ones climbing over the fence at the zoo because the frame of the bear exhibit is really better just a couple steps beyond the fence.
The relationship between artists and rules has always been tenuous and contentious at the best of times. Yet the Rule of Thirds ranks right up there as one of the more time-tested concepts in composition, both in photography and in the art world long before photography came into existence.
The general concept is fairly straightforward: Divide the image frame into nine equal sections. Position your subject at the intersection of the dividing lines. Which one of the intersections will depend on what else is in the frame.
The horizon line can be higher or lower, depending on whether you want to focus attention on the foreground or the sky, anywhere but along the center line.
Subjects In Motion
If your subject is in motion, the Rule of Thirds changes somewhat as you want to give your subject room to move in the photograph. Position the subject so their direction of motion is toward the open area of the picture. If a subject is moving left to right, you generally don’t want to frame the subject in the lower right hand corner as it leaves the impression they’re running off the frame.
For every rule there are exceptions. I have seen some pictures when a slow shutter speed was used and the subject positioned at the distant corner, relative to their direction of motion, to make it appear as if they were going so fast the camera could not pan fast enough to keep up with them.
So there are rules and then there are rules in photography. Learn them, break them, find new ways to apply them to your own personal style. At least no one is going to issue you a ticket for climbing on the street light.