The process (both science and art) of arranging visual elements within the viewfinder of your camera to create something hopefully beautiful, or to at least communicate your message. There are "rules" to help you, but these are merely guidelines a skilled videographer, cinematographer, or photographer uses to help him or her get things set up initially.

There are some important characteristics of shot composition:

That was more of the artistic portion of composition. The scientific part includes stuff like:

For the stuff I just mentioned, please note that:
  1. This isn't strictly scientific stuff; more like the use of technical considerations to embellish the artistic intent;
  2. This isn't strictly shot composition, but maybe more general filmmaking or videography technique.
However I think it still applies, and is worthwhile to mention here.

I mentioned some "rules" earlier. The most important and most widely-used is the rule of thirds. But again, like I've said, this is something that is artistic and creative. These rules are a good starting point -- nothing more and nothing less.

Please don't just downvote without /msg'ing me. I'd appreciate the feedback