"What is design? A plan for arranging elements in such a way as to best accomplish a particular purpose." - Charles Eames
The purpose of two-dimensional design is visual communication.
Design is both a noun and a verb - it describes the thing created as well as the process of creating it.
A design is created with elements - line, shape, color, value and texture - that are put together using principles - unity, variety, emphasis, balance and scale.
Although design can be divided into elements and principles for the sake of discussion, it is only when these elements and principles work together to form a whole that a design is considered successful.
The credit for analyzing forms and structuring design theory goes to the Bauhaus, a school founded in Germany in 1919. The Bauhaus developed a fundamental grammar of the visual, of which the central elements - the ABCs, so to speak - were the trio of primary colored shapes 
.
The metaphor the Bauhaus used is fitting; the elements of design can be compared to the elements of writing - words and punctuation - and the principles of design can be compared to the rules of grammar.
Design, like writing, involves problem solving, planning and organizing. In verbal communication, we choose which words to use and how to put them together to best communicate our thoughts and ideas. In visual communication we choose which elements to use and how to put them together to best communicate our thoughts and ideas.
We would not randomly throw words and punctuation on a page and expect them to communicate.
Should we do the same with images?