It's shorter than prose, it's generally more vivid and expressive than prose, and it's often more accessible to readers, even if it's just one image or the sound of a phrase. More importantly, poetry is designed to appeal to the senses and emotions, two things which are meaningful to any audience.
I think poetry appeals to so many people because poetry is a means of expression. I also think that this is the reason that people write poetry. You can express your feelings in very creative and unique ways. I have found that many of students like to write poetry as well. It is fun for them and they really get motivated by it.
The same reason that music or art do - it is a form of expression that uses creativity, artistry, inflection, arrangement, and on and on. It is language in art form. For me, it is a way to boil away all that is unimportant in communication and leave only the barest, most honest words possible. It's refreshing.
I enjoy reading and writing poetry because of the structural diversity and freedom it allows. It's also a great way to write what's on your mind at any given time. To rhyme or not to rhyme--that is dependant upon the mood or inclination. Practicing various forms (sonnets, haikus, etc.) are both creative and challenging.
There seems to be a very universal quality and approachable quality to poetry. I think its appeal is based on the idea that it can be so very subjective. Yet, within this particular realm is where its greatness might lie. Its subjectivity might be key to its objective, or universal, appeal. The Romantic thinkers might have gotten this one right. In expressing the subjective experience, poetry allows a universal moment to be shared. This idea might be what makes poetry appealing to such a broad base of people. The notion of being able to universalize the personal, externalize the subjective helps to convey an experience about poetry and in this light, one can see greatly where appreciation of it might be advanced.
As an art form, poetry is an expression of our understanding of our world. And because it is typically concise, figurative rather than literal, rhythmic, and generally aesthetically pleasing to the ear, it is often more memorable than other forms of communication.
The metaphoric and figurative nature of poetry also lends it to multiple interpretations and personalized application of those interpretations based on the lives and experiences of each individual reader. In this way, each of us can find something relevant and personal in a poem making the genre much more flexible than others.
Poetry is language of the heart. As such, it elicits emotional responses and, thus, inspires, consoles, commiserates, awakens, and communicates. And, as mentioned in the previous post, poetry does this in a compact form that can be easily accessed and read frequently.
Another appeal of poetry is its freshness of expression and uniqueness, for there is a certain enjoyment that readers feel as they see what they have observed expressed in different and creative ways. And, unlike prose, poetry has an auditory appeal as well as cerebral and emotional.
I think one of the appeals of poetry is that the reader can get a great deal of imagery and information in a compacted form that is rhythmical and easily remembered.
In the modern world, poetry appears in the lyrics of the songs that we listen to on the radio. You can look at the wide demographic that enjoys poetry in the same was as the diverse assortment of listeners who enjoy songs on the radio. Just as there are many different styles of music that appeal to different people, there are also many different styles of poetry that reach a divergent audience. There are love poems, political poems, spiritual poems, happy poems, sad poems.
For just about every action, feeling, thought, or emotion, you can find a poem that expresses it concisely. Poetry allows us to experience the world around us, to share feelings and experiences, and to express ourselves through words.
Perhaps the basic reason is that Poetry is essentially about feelings which almost all human hearts are so sensitive about. Secondly, Poetry is the most creative and the most condensed use of language, language made up of images, symbols, figures of speech, rhyme and so on. Thirdly, Poetry is truly, what Auden has said, 'memorable speech'. Fourthly, there is a strange universality in the expression system that Poetry generates so artistically and yet so spontaneously. We must remember that in all languages Poetry came first, as if synonymous with creativity. Eliot was absolutely correct when he observed that 'genuine poetry can communicate before it is understood'.
I think one of the reason for poetry appealing to so many different people is that poetry is of so many different types that almost everyone is able to find poetry to math his or her tastes. I do not think that without such variety poetry, or for that matter even other forms of literature would have been very popular.
The most attractive feature of poetry that is not present in any other form of literature is the presence of rhythms and rhyming. Also poetry scores over prose in its ability to say things more interestingly, because it is less constrained by rules of grammar.