The "Rule of Gaze" is used a lot in compositions where the subjects are people and/or animals.  The rule tells us that we need to leave space beyond the frame for their gaze to fix - whether that is directly at the viewer or at something seen or unseen in the photo.

Direct gaze when the subject is looking at you invites an intimate, personal interaction.   You form a connection with the subject, compelling you to engage, forming a bond with the subject.  It feels comfortable.

When the gaze of the person or animal is averted it can lend a sense of introspection and mystery.  It makes the viewer part of the story, invoking curiosity about what the subject is looking at and creates narratives and interpretations for the viewer to explore.  

There is also the ability of the photographer to convey gaze in inanimate objects, allowing them to take on a human quality:  a swing with space out in front of it, a car moving along the highway, a tree standing on a ridge with the expanse of the landscape in front of it.

Who or what will you photograph today and apply "The Rule of Gaze"?  And remember to give it directional space.