A simplistic way to look at writing is to say that writing is either poetry or prose. This makes sense if a person uses a very strict definition of both types of writing. The Merriam-Webster Dictionary defines prose as "distinguished from poetry" through its usage of "ordinary" and "everyday" speech. The definition also mentions the constantly changing rhythm (which may seem to be a lack of rhythm). By definition alone, poetry stands out in sharp contrast because it heavily emphasizes verse and meter. Breaking the writing into stazas is also a major part of the definition of poetry.
The two forms of writing seem to be miles apart, yet poetry like free verse begins to blur the line. Plenty of free verse poems are not divided into separate stanzas. By definition, free verse doesn't use regular rhyme, rhythm, or meter. This makes free verse look or feel like prose to a lot of students, and I've had students flat out say that free verse is not poetry because it doesn't have rhyme and meter. They don't care if the lines are short, the writing is broken into stanzas, or that lines of verse might not have subjects and verbs: they are sure that poetry must have specific structures.
If a key piece of prose is sentence structure, prose poetry shouldn't be possible; however, when you look at a secondary definition of poetry, prose poetry all of a sudden seems possible. Here's the secondary definition:
writing that formulates a concentrated imaginative awareness of experience in language chosen and arranged to create a specific emotional response through meaning, sound, and rhythm
Notice how this definition doesn't emphasize structure. It emphasizes words, imagery, and economy of language. This means that if a writer takes those elements and puts them in sentence and paragraph form, prose poetry is the result. Check out the poem "[Kills bugs dead]" by Harryette Mullen for a good example.