Unlike a poem, it's highly unlikely anyone will ever want to set one of your essays to music. While some poems may set out to accomplish the same goals as an essay, such as presenting an argument or telling a story, the structure, common techniques, and basic rules required for an essay are quite different than a poem.
No matter what type of essay you're asked to write, such as argumentative, expository, descriptive, or narrative, there are usually structuring requirements that must be applied. An introductory paragraph that presents your ideas, a body that lays out each of those ideas clearly, and a summary paragraph that presents some type of conclusion are the common requirements for most traditional essays.
Poems, on the other hand, can vary widely in structure. Haikus, sonnets, limericks, and ballads are all forms of poetry and each is defined by its unique and specific structure. Poems can rhyme or not rhyme, be freeform or limited to a certain number of syllables, and they can fill a book or be written in 14 lines of iambic pentameter.
Techniques for writing a good essay include presenting ordered points that relate back to a single thesis statement, writing interesting and relevant topic sentences to present ideas for each paragraph, and presenting excellent supportive references from outside sources.
Poems, on the other hand, use alliteration, creative similes and metaphors, onomatopoeia, assonance, and rhyming lines. However, many poems include none of these. Unlike essays, there are no universal techniques used in good poetry. Creativity wins the day over following hard and fast rules.
Anyone who has ever submitted an essay assignment knows that grammar, spelling, and punctuation are key in a good essay. Every sentence should end with the proper punctuation mark, creative spelling is frowned upon, and an essay writer should proofread to ensure subject/verb agreement, sentence structure, and use of proper English.
In poetry, rules like these are often tossed out the window. Entire poems can be written with nary a punctuation mark in sight, and the creative use of language is encouraged.
In short, poems allow for a lot more creative freedom and can include a wide range of possible structures and techniques. An essay makes logical points that should be clear to anyone who reads it. Even the best poems, however, sometimes make sense to no one other than their authors.