For meanings, I'll start with Poetry.
Poetry is when you impose structure on language -- rhyme, imabic pentameter, the sestina, etc. -- or, when you create additional layers of meaning beyond the immediate meaning of the phrases: e.g., the arrangement of the words on the page, or the timing of words spoken; phonetic effects created by the sounds of the words, etc.
My working definition of prose, for now, is simply a negative one: language without imposed metrical structure, and without additional layers of meaning.