Rhyming is not a prerequisite for poetry. In fact, rhyming poetry was popular for a relatively short period in a relatively specific part of the world. Poetic forms are generally culturally defined, and more often involve cadence, word play, and organization of themes. The ancient Hebrews emphasized repetition and contrast, the Japanese liked syllabic symmetry, and the Anglo-Saxons made extensive use of alliteration and assonance.
Asserting that one form of poetry is better than another is no more than snobbery, but to claim the opposite (that true poetry has no form) is equally unreasonable and narrow. Of course poetry has form: how else could it communicate?
Understanding poetry's different modes is an important step toward understanding poems themselves. Do you have to know that a Shakespearean sonnet always has three quatrains and a couplet to enjoy it? No, but it helps, as does knowing that the final two lines constitute a volta, a shift in attitude or imagery toward resolution of the problem presented in the previous stanzas.
It also helps to know not all sonnets follow this form, and that a sonnet isn't really a sonnet if every line isn't exactly ten syllables long, following a stressed/unstressed pattern known as iambic pentameter. In turn, iambic pentameter is an important term to know if you plan on writing a villanelle, since its lines follow the same scheme. The interrelatedness of terminology can be both helpful and frustrating, but wallowing around in a sea of roundels, enjambment, slant rhyme, and dactyllic hexameter will be nothing but frustrating unless you learn what all those words mean.
Some people think it's not worth the effort and never bother. Which is fine, if you don't intend to read or woo women. If poems only existed to put words together in audibly attractive ways, such a dismissive attitude would be fine. If, however, poems are messages to the soul, being able to interpret them and identify one type from another becomes much more valuable.
One could even say imperative. Most of the world's greatest poets have adopted the popular or accepted forms of their cultural context, and whether they were aware of it or not when writing, these forms influenced not only the messages, but the way those messages were expressed. Certainly, one can enjoy Keats without understanding all the technical elements in his work; but one can enjoy Keats even more when those elements are understood.
We carry books that explain terms, books that equip readers for interpretation and analysis, even books that help you write your own poems. More importantly, we carry books of poems by the practitioners of the elements and forms discussed in those instructional works. In the end, there's no absolutely wrong way to read poetry, just wrong ways not to read it.