The elements of poetry include meter, rhyme, form, sound, and rhythm (timing).
Different poets use these elements in many different ways. Some poets do not use rhyme at all. Some use couplets, while others may rhyme the second and fourth lines only...in a stanza.
Some use stanzas (form), which are often lines of four, grouped together—but poems can also be broken into sections consisting of eight lines or eleven. It depends on the author. In Shakespeare's Sonnet 29, for instance, the first and third lines rhyme, as do the second and forth—he uses three four-line stanzas, ending with a rhyming couplet (pair of lines):
When, in disgrace with Fortune and men's eyes,
I all alone beweep my outcast state,
And trouble deaf heaven with my bootless cries,
And look upon myself, and curse my fate...
One aspect of poetry that many poets use is sound. It is here that you find use of literary elements: alliteration, assonance, consonance, onomatopoeia, etc. This devices appeal to the ear—the sound is an important characteristic because it gives poetry a musical quality. (Rhyme also uses "sound.")
Figurative language is essential to poetry. This is found with similes, metaphors, metonymy, hyperbole, personification, etc. However, it is important as a characteristic because poets endeavor to create an image in the reader's mind, so that the reader is moved in some way—able to envision the picture (and even experience an emotion) the author is trying to reproduce. Look to William Carlos Williams' "The Red Wheelbarrow." There is no rhyme; it is very short. But the imagery it creates is quite impressive:
so much depends
a red wheel
glazed with rain
beside the white
There is no rhyme, but the senses pick up the color of the wheelbarrow, the slick surface from the rain, and the contrast in color between the red wheelbarrow and the white chickens. With regard to the characteristics of poetry, look deeper—the poet is still telling us that what seems simply picturesque by description will work hard in the hands of the gardener or farmer. In this case, it is easy to see that the author is also conveying an even deeper message or theme: do not be deceived by outward appearances...or..."don't judge a book by its cover."
The intent of the poet may be to praise love, lament heartbreak, glorify nature, tell a story (epics like Beowulf, or Coleridge's The Rime of the Ancient Mariner), or even attempt simply to entertain. However, a poem's "success" relies on a reader's reaction to the work. The poet will use poetic devices to this end. The poet will also endeavor to share some message or deeper meaning with the reader, and in this way, create a connection between the poem and the reader, making the work memorable...appealing to common emotions: joy, love, fear, longing, sorrow, etc.