Most of us think of Poetry as ryhming or at least have a meter or beat, but free form poetry is considered poetry and does not have to meet either requirement. I would most likely define poetry in relationship to prose. Prose tells a story of some kind. It has a beginning middle and end, even if it is short or not very detailed or leaves us hanging. Poetry expresses thoughts and feelings without having to have any chronology or any specific story or event that it is describing. I find a lot of poetry difficult to read or relate to, because I don't know what the poet is trying to express or I can't relate to what they seem to express. I love the poetry of lyrics though and any poet who can make me see and feel what they feel, I do enjoy.
I believe that a poem is a song with no music. Poems tell stories and are a way of expressing your emotions; you have to read between the lines of poems to really understand what message it is trying to convey. Poems often rhyme to make them more beautiful. For example, in a love poem, to evince that couples come in pairs as do rhyming couplets. A love poem can describe how two people cannot be without each other and feel that they complete one another simply by using rhyme.