When you are framing people within your shots, using the Rule of Thirds should encourage you to leave an appropriate amount of looking room (also known as lead room) and head room.
Looking room is the space that the subject is looking towards in the frame. Usually, your subject – either a character in a narrative, or an interviewee in a documentary – should be looking into a majority of the frame. If you are using the rule of thirds, your character will have about 2/3 of the frame that they are looking into.
Head room is the amount of space that is between the top of the subject’s head and the top of the frame. Again, if you are using the rule of thirds and placing the character’s eyes in the top third of the frame, then you should find that you are leaving a conventional amount of head room in the shot.
These two concepts are the reason why you usually see interviewees looking not directly at the camera, but just to the side of the camera, with more of the empty frame in the direction in which they are looking.
To learn more and for some examples, see the three videos below.
Lights Film School talking about both looking room and head room:
D4Darious on looking room:
D4Darious on head room:
Other Shot Composition pages on Opening Class: