Examples:
The above is a bad example of the Rule of Thirds due to the fact that the person is positioned in the centre of the screen. This is not the viewers focus point as we don't tend to look directly in the middle. Also the person is wearing a dark blazer which blends in with the background so it is hard to see him.
The above picture is a good example of the Rule of thirds rule due to the fact that the person is positioned more to the left of the image where the intersections of the lines would be. This is the audiences main focus point so it will grab their attention almost instantly. Not only this but the light coming from the end of the tunnel makes the person more visible and he is away from the dark shadow on the right.