Wondering what poetry IS is one of the things that makes me most scared to write it. Or at least to share it under the label of "poetry". If I express something from deep in my soul, whether I take time to frig around with the words and make it rhyme or whether it's just a free-form spill, and I believe it is poetry, does a reader then get to say, "no, actually it isn't"? This fear is always there, and it tells me I'm a fraud and that all my so-called poems should just stay private in my therapeutic journal where they belong.
So, for me, poetry is a seeking for connection. Connection with other people, by saying stuff that so many of us feel but don't dare say, and saying it in a way that brings the reader to my vantage point so we can look out over the scene (concept, idea, situation) together and come to some understanding. I've written my train-of-thought angst in journals for years, but only when I started sharing it (which means I had readers in mind during writing) did it turn into something anyone could call poetry. Or did it?? Crap, I don't know. It's still a lot of artsy-fartsy bullshit.
Maybe it would be more concise to say, poetry is just spitting in the face of our own aloneness, using words. And applying to those words "artistic and aesthetic intentions and objectives" (as mentioned a few comments above) - which to me means it has a reader in mind and a desire to connect with them.