The rhythmic structure, or metre, is important in poetry. It affects the pacing and flow of motifs through a piece of poetry, specific structural forms help you decide what type of poem it is but modern poetry doesn't always stick to rigorous forms. End rhymes and assonance, where vowel sounds are repeated in a line, are useful for reinforcing motifs but a poem is meant to be spoken aloud so the structure plays a large part in the meaning and impact of a piece of poetry.
It's been a while since I studied poetry so I'd need to brush up on terms to dissect a poem throughly but if you search for those terms you should find good resources.