The rule of space is widely known as "rule of gaze" or even as "lead room" in some photography scenarios, but isn't as renowned as other compositional rules such as the rule of thirds. However, numerous photographers wisely utilized this technique without even it.
In simplest sense, the rule involves generating a negative space that directly relates to your subject in some way.
While in practice, the rule involves the use of actual space in a photo, it is really used to convey an idea or an implied movement, action or thought. Since everything that is in a photo should be there for a reason and should relate to the subject, the presence of space in a photo doesn't automatically mean that the rule of space was being consciously utilized.
Empty space in a photo that doesn't in some way support the composition and relate to to the subject can actually ruin what had the potential to be a good photo.
Creating a Sense of Size and Perspective
The rule of space can be used to imply a sense of size or perspective.
In this photo the large and fairly nondescript negative space around the boats conveys a feeling of vastness and grandeur in the environment while making the boats appear smaller.
Here is an even more dramatic example. The boats and the island would appear large to us if it were close. The large amount of space around it shows how small it really can be comparatively.
Implying Movement and Speed
The rule of space is a wonderful way to convey movement and speed in your subject.
In this example, the space in front of the person kayaking conveys both movement and perspective, and lets us know that the kayak is soon to be on its way up.
This photo is an excellent example of the rule of space conveying movement and speed. There is an active space in front of the runners that lets you know that they will be moving into that space.
The rule of space can be used to convey where the subject has been as well, rather than where they are going. In this example, there is quite a bit of dead space behind the festival queen and very little active space visible in front of her. She is walking away from the camera and on her back is a dead space showing her previous location in space.
What is the Subject Gazing At? What are They Thinking?
One common way to add depth and intrigue to a portrait where the subject is not looking directly at the camera, is to add some negative space in the direction of the subject's gaze. There should be enough space for the subject to look into and not appear crowded. Viewers of the photograph will naturally also look into this space and wonder what might be going on outside of the photograph. For example, if the subject is smiling and looking off in the distance the viewer will wonder what she is smiling at.
This picture of an old man in the park is a good example of the rule of space, or rule of gaze, at work. He is obviously resting with his shoes off his feet, and something caught his attention… perhaps at a pretty lady.
In this photo of a cat looking to its side, we are left to wonder what caught the cat's attention. Probably another cat or a prey. Without the negative space on the right, this photo would have much less impact.
Perhaps you have already been admiring the rule of space and even using it in your photography, either consciously or unconsciously. Whatever the case may be, incorporating this rule of composition will surely improve the impact of your photos.