Composition is the orderly arrangement of elements in a scene which, when taken as a whole, conveys intent and meaning.
That's one definition; another says a composition is a conglomerate of innumerable forces, many of which function subconsciously. If this is true, then studying composition should provide the framework for making better "conscious" decisions while shooting.
Good composition allows us to quickly understand a photograph. In essence, our eyes are guided by the elements of the composition as we search for content in the photo.
Compositions can be closed or open.
Compositions can also be static or dynamic (implied motion).
We understand a composition first by a perception of its elements and then by a perception of relationships between the elements. Therefore we'll look at