The example to the right follows this rule but it is still not an acceptable shot from a photographer's standpoint. Why? The bird is running out of the picture. A better composition would have been to frame the bird on the far right and have it running into the picture. That way, the bird has somewhere to run and viewers are drawn into the picture instead of out of it.
Any time a subject is in motion, it is a good idea to compose the picture so that the subject enters the frame as in this example. The dolphins are coming out of the water into the frame and you can almost imagine them completing their jump and splashing into the water on the other side.
This rule doesn't just apply to subjects in motion. Any time the subject is looking to one side, the image should be composed with her/him looking into the picture. The bird's body in the image below is pointed to the left, but the bird is looking to the right. Composing the bird to the left of the frame gives the feeling of the bird looking into the picture instead of out of it.
It is important to think about composition when shooting as it may make the difference between a snapshot and photograph.
