The Rule Of Thirds has been used for centuries and is a common filming method to make shots look more professional. This technique was originally used in paintings.
If you imagine a tic-tac-toe looking board or 3×3 grid over the picture or video, the subject or main object should be located on one of the lines and not in the center square. This often gives the pictures or clips a more satisfying and professional appearance to them and can usually improve your filming.
It is also useful to align things with the individual lines. For example, when the subject is a human, it might be a good idea to align both eyes along the top horizontal line. This technique can also be used with the horizon. Placing the horizon along the top line emphasises something on the ground with the camera possibly looking down. Placing the horizon along the bottom line emphasises the sky and clouds.
In many cases, it is more comfortable to the eye if the subject has more room in the frame to move around. Be sure to leave room above your subject so it doesn’t seem it’s head is being ‘cut off’. This is called ‘Head Room’. Also, generally you’ll want to leave more room in front of your subject than behind. This especially holds true if the subject is moving horizontally across the frame. The audience wants to see what is in front of the subject. When the subject is static, it is less necessary to place the majority of the frame in front of the subject. However, you don’t want the subject’s ‘nose’ to look like it is pressed up against the side of the frame. Give the subject some room to ‘breathe’. This is usually called ‘Nose Room’.
It would seem likely that the Rule Of Thirds is based upon Fibonacci’s Golden Ratio. If you consider a line divided into two unequal segments, the longer one being 61.8% of the entire length then the ratio of the shorter segment’s length to the longer’s would be that same 61.8%. This balance between the different sizes is a recurring theme in art and nature and is very pleasing to the human eye. It is reasonable that the Rule of Thirds is a simplified version of the Golden Ratio.