Don’t feel bad. I have an advanced degree in English and I’m not sure I understand poetry.
The best beginning I can come up with in explaining it is that poetry is a sort of mis-mash of prose and drama. We typically think of a play as something meant to be performed (or at least read aloud) and prose, while it lends itself well to oral utterance, does not inherently require itself to be read aloud.
Poetry generally isn’t meant to be a dead medium–the experience of it is supposed to add up to more than just the words on the page. While you can ‘get’ a piece of information delivered in written prose, it may not be possible to ‘get’ a poem unless it is uttered.
Of course, that’s still not a requirement, as many poems–particularly the ones we can organize by rhyme, but also free verse–are just as good on the page.
In a lot of ways, poetry can be as enigmatic as language itself. Just like a lot of the grammar questions on the dope sort of devolve into bickering about ‘style,’ trying to define poetry is sort of like trying to rope the wind.
For me, I take poetry to mean a work that depends on not simply information, but an aesthetic experience. So, for example, in this post I am giving you spaces between words, and line breaks between paragraphs, and punctuation; however, all of that is more or less incidental. What I’m trying to do is convey information–my spacing and punctuation just make it easier to organize.
Poetry, though, means that things as simple as word choice matter–and matter a lot. Even the spaces of poems matter. They’re not there to specifically follow a convention. They add to the aesthetic experience.
Take enjambment, for example, where a phrase or thought is broken by a line break (so that the thought ‘straddles’ the line break.) Shakespeare gave us:
I am not prone to weeping, as our sex
Commonly are; the want of which vain dew
Perchance shall dry your pities; but I have
That honourable grief lodged here which burns
Worse than tears drown.
Those lines are enjambed. This gives emphasis to the word at the end of each line (rather than the word at the end of each phrase/thought.) Shakespeare apparently wanted us to notice the word “sex” moreso than the word “are”. Why he wanted that…well, that’s up for discussion.
Lots of times, iambic pentameter requires enjambment, or at least weird spacing, to keep the rhythm going. That’s why you’ll see some characters’ lines spaced to the right of the previous character’s ending line.
Anyway–we can generally speak in terms of aesthetics, word choice, spacing, structure, punctuation…etc. because all of those are more conscious choices on the part of the poet than all of those things in prose. And, while there is undoubtedly metaphor, metonym, symbol, and so on in prose, they take on a greater weight in poetry.
I’m not sure if any of this helps, and there will be dissenters, but it’s all I’ve got.