I recall reading, in my salad days, a number of interesting definitions of "art," "music," and "poetry." What I mainly remember about these definitions is that, with each successive attempt, the authors increasingly tied themselves in more knots to deal with complexities arising from modern experiments in color and line, tonality and structure, meter and form. Often the result was a definition that was either useless in its abstractness or so lengthy and complicated that it defeated the purpose of defining anything. As I understand that purpose, a definition should be short, simple, and useful. I appreciate the difficulty of making such a definition apply to the variety of things that have hitherto taken refuge under the banner of, say, "poetry." Nevertheless, I think it's doable.
To start with, our language has two key names for the same art form: Verse, on the one hand; and Poetry, on the other. I think it might help things if we explored them as distinct concepts. It's also interesting to point out how other languages cope with the naming of this thing. For example, the Russian word Shtihi, with a nice guttural h similar to the German ch, suggests an analogy to the obsolete English word Stich, which in turn comes from Greek. In either English or Greek, this word can mean either a row (of trees) or a verse (of measured poetry or of Scripture).
A rough synonym for either sense of the word "stich" might be Line. And this, in turn, suggests a short, simple, useful distinction between Prose and Verse. While the former organizes thoughts into grammatical structures (sentences, paragraphs), the latter organizes them in lines. Whether these lines are metered or free, rhyming or blank, arranged in stanzas or continuous, indented or blocky, restricted to one typographical line or allowed to wrap, are all accidental modifications of the one essential fact about Verse: it is the organization of thoughts into lines.
There are several reasons I think it is helpful to distinguish this concept from Poetry. And none of them is that the definition of Poetry needs to be less simple, brief, and useful. One reason is that I don't think this concept of Verse as "language arranged in lines" sufficiently covers what one intuitively understands Poetry to be. Another reason is that one can imagine, and with a certain amount of experience one is almost certain to encounter, either cases of Verse that are not Poetry, or cases of Poetry that are not Verse. So what is Poetry, regardless of whether or not it is also Verse? I think it is the use of unusual language to give special significance to a thought.
The "unusual language" clause in this definition covers a broad range of rhetorical effects such as figures of speech, plays on words, the use of archaic terms and foreign borrowings, and metrical patterns such as alliteration and assonance. Meanwhile, the "special significance" clause is broad enough to encompass a range of meanings, all the way from "sacred oracles" to "greeting-card sentiments." It isn't a judgmental definition. Any judgment of what does or doesn't constitute as "unusual language" or "special meaning," is a gloss on the definition that a given interpreter may freely apply in specific cases, subject to a difference of opinion. But in my opinion, the definition itself rises above differences of opinion.
And so the distinction between Verse and Poetry can become clear, especially when you imagine possible conflicts between the two. Adding line-breaks to an ordinary, banal paragraph may or may not make it Verse, but it certainly does not make it Poetry. On the other hand, a paragraph written with exquisite care and full of interesting word-choices and thought-figures might deservedly be called Poetry, though it clearly is not Verse.
Another way to spot the distinction is to observe works that are both Verse and Poetry, but that succeed as one while failing at the other. Again, the interpreter's opinion is crucial here. Poets like E. E. Cummings could write Verse that was all but unreadable but which, when read aloud, struck chords in the heart and mind that only Poetry can reach. The arrangement of the lines may look as though a typewriter took a crap on the page, yet the words themselves convey a powerful thought in a unique way. On the flip side, you get writers like Ogden Nash, whose Verse forms sparkle with wit and originality, while the effect of his Poetry is often little more than a mild groan, as at a lame joke. Robert Service and Rudyard Kipling are both masters of conventional and even tedious verse forms in the service of colorful language and sometimes overwhelming emotional effects; while many a college literary magazine can boast examples of fascinating verse-form experiments that utterly fail to deliver originality in either word or thought. Good Verse can be bad Poetry, and vice versa.
A third way to perceive the distinction between Verse and Poetry is to observe that they have different opposites. We have already contrasted Verse with its opposite, which is Prose. The opposite of Poetry, however, is not Prose, properly speaking. The opposite of Poetry is something more like "banal, everyday language."
I think this distinction and two-fold definition can also help to properly define "art" and "music." Maybe the trouble critics and theoreticians have, arriving at a "short, simple, useful" definition of these things, is that they are trying to define one thing by itself rather than a relatively successful integration between two things. Art isn't just the decoration of space through the manipulation of visible materials, nor is it necessarily a visual representation of something intelligible to the human mind. Music isn't just the decoration of time through the manipulation of organized sound, nor is it necessarily a perceptible structure of rhythm, harmony, and memorable tunes. Maybe, in each case, we're talking about two things that work best when they go together. I'm thinking of something like the ratio between the structuredness of thoughts in time or space and the intelligibility of units of visual or aural language when organized within that structure. I don't have my thoughts on this completely in order yet, certainly not enough to arrive at one or two (or four) short, simple, and useful definitions; but it's something to work on.