Compositions are, by definition, arrangements of one or more elements or forms. This definition therefore presupposes that those elements or objects are somehow distinct from one another: e.g. a series of lines, a combination of text and image, or a movie poster with the title of the film and the different characters in that film, etc.

But this presupposition is a dangerous one. Elements actually need to be carefully designed with a solid awareness of principles so that they can be distinguished from one another. Not just distinguished as being separate, but distinguished in terms of importance! Contrast between elements makes their distinction clear, and allows the eye and brain to flow between these distinct elements from the mot important to the least important.
Even in the most basic web page or word processing document, without any advanced styling whatsoever, there a basic ways to use size to contrast between things like headers, sub headers and body text:
The first web page ever!
yucky Word...

But besides these utlitarian uses of contrast, this principle is also a key way to make a composition more interesting. Below is the same word processing document that uses only scale and weight to provide contrast, side by side with the same content with more lively and decisive contrast between various elements:

Screen Shot 2017 06 30 at 1.17.45 PM
vom dot com
Screen Shot 2017 06 30 at 1.41.56 PM
pro.fo.sho!

Lastly, contrast is how one creates a focal point in a composition, as seen here in this very famous poster by French illustrator and barfly Henri de Toulouse-Lautrec. Because of its dark value, large size, and highly contrasted yellow eyes, the titular cat is the first thing that grabs our attention.

Henri de Toulouse-Lautrec, 1893.