Alliteration

The repetition of the same consonant sounds at any place, but often at the beginning of words. Some famous examples of alliteration are tongue twisters. 
She sells seashells by the seashore, Peter Piper picked a peck of pickled peppers.

Assonance

The repetition or a pattern of (the same) vowel sounds, as in the tongue twister:
"Moses supposes his toeses are roses."

Ballad

A poem that tells a story similar to a folk tale or legend and often has a repeated refrain. The Rime of the Ancient Mariner by Samuel Taylor Coleridge is an example of a ballad.

Carpe diem 

A Latin expression that means "seize the day." Carpe diem poems urge the reader (or the person to whom they are addressed) to live for today and enjoy the pleasures of the moment. A famous carpe diem poem by Robert Herrick begins "Gather ye rosebuds while ye may . . ."

Couplet 

In a poem, a pair of lines that are the same length and (usually) rhyme and form a complete thought. Shakespearean sonnets usually end in a couplet.

Elegy 

A poem that laments the death of a person, or one that is simply sad and thoughtful. An example of this type of poem is Gray's "Elegy Written in a Country Churchyard."

Enjambement

A line ending in which the sense continues, with no punctuation, into the following line or stanza.  

 "But in contentment I still feel

  The need of some imperishable bliss."

Feminine rhyme

A rhyme that occurs in a final unstressed syllable: 

pleasure/leisure, longing/yearning

Haiku

A Japanese poem composed of three unrhymed lines of five, seven, and five syllables. Haiku often reflect on some aspect of nature.

Hyperbole 

A figure of speech in which deliberate exaggeration is used for emphasis. Many everyday expressions are examples of hyperbole:
tons of money, waiting for ages, a flood of tears, etc.
Hyperbole is the opposite of litotes.

Imagery 

The use of pictures, figures of speech and description to evoke ideas feelings, objects actions, states of mind etc.

Limerick 

A light, humorous poem of five lines with the rhyme scheme of aabba.

Litotes 

A figure of speech in which a positive is stated by negating its opposite. Some examples of litotes:
no small victory, not a bad idea, not unhappy. 

Lyric

A poem, such as a sonnet or an ode, that expresses the thoughts and feelings of the poet. A lyric poem may resemble a song in form or style.

Masculine rhyme

A rhyme that occurs in a final stressed syllable:
cat/hat, desire/fire, observe/deserve.

Metaphor 

A figure of speech in which two things are compared, usually by saying one thing is another, or by substituting a more descriptive word for the more common or usual word that would be expected. Some examples of metaphors:
the world's a stage, he was a lion in battle, drowning in debt, and a sea of troubles.

It is probably the most important figure of speech to comment on in an essay.

Narrative

Telling a story. Ballads, epics, and lays are different kinds of narrative poems.

Ode 

A lyric poem that is serious and thoughtful in tone and has a very precise, formal structure. John Keats's "Ode on a Grecian Urn" is a famous example of this type of poem

Onomatopoeia

A figure of speech in which words are used to imitate sounds. Examples of onomatopoeic words are:
buzz, hiss, zing, clippety-clop, cock-a-doodle-do, pop, splat, thump, tick-tock. 

Another example of onomatopoeia is found in this line from Tennyson's Come Down, O Maid:
"The moan of doves in immemorial elms,/And murmuring of innumerable bees”

The repeated "m/n" sounds reinforce the idea of "murmuring" by imitating the hum of insects on a warm summer day

Pastoral 

A poem that pictures country life in a peaceful, idealized way.

Personification 

A figure of speech in which nonhuman things or abstract ideas are given human attributes:
the sky is crying, dead leaves danced in the wind, blind justice.

Refrain

A phrase, line, or group of lines that is repeated throughout a poem, usually after every stanza.

Rhyme 

The occurrence of the same or similar sounds at the end of two or more words. 

The pattern of rhyme in a stanza or poem is shown usually by using a different letter for each final sound. In a poem with an aabba rhyme scheme, the first, second, and fifth lines end in one sound, and the third and fourth lines end in another.

Rhyme scheme

The pattern that is made by the rhyme within each stanza or verse.

Simile

A figure of speech in which two things are compared using the word "like" or "as." An example of a simile using like occurs in Langston Hughes's poem ‘Harlem’:

 "What happens to a dream deferred?/ Does it dry up/ like a raisin in the sun?"

Sonnet

A lyric poem that is 14 lines long. Italian (or Petrarchan) sonnets are divided into two quatrains and a six-line "sestet," with the rhyme scheme abba abba cdecde (or cdcdcd). English (or Shakespearean) sonnets are composed of three quatrains and a final couplet, with a rhyme scheme of abab cdcd efef gg. English sonnets are written generally in iambic pentameter.  The volta  (“break”) marks a change in the initial line of thought or feeling at the end of the octave or eighth line.

Stanza 

Two or more lines of poetry that together form one of the divisions of a poem. The stanzas of a poem are usually of the same length and follow the same pattern of meter and rhyme.

Stress 

The prominence or emphasis given to particular syllables. Stressed syllables usually stand out because they have long, rather than short, vowels, or because they have a different pitch or are louder than other syllables.

Symbol

When a word, phrase or image 'stands for' an idea or theme.  
The sun could symbolize life and energy or a red rose could symbolize romantic love.