Contents:
What is poetry? (not)1
Modes of thought: science and poetry1
Note on subjectivity2
Science and poetry2
But what is poetry?3
How to read a poem4
Learn the music4
Change of consciousness5
Plain vanilla meaning6
It is worth it7

What is poetry? (not)
Everybody knows what poetry is.  It's that pokey, confusing kind of writing, where you never know where you are in the sentence, and it's all sing-song, like a jump-rope rhyme.  If it's "good" poetry, you can't figure it out; if it's children's poetry, it's just boring.
?
Since I helped my mother get some of her thoughts about Emily Dickinson into print, and then took up the task of marketing it, I have been deeply disquieted about the poetic illiteracy of our world.  This essay is a brief attempt to express what is wonderful and valuable about poetry.

We need to understand
1. The poetic (and the scientific) modes of thought,
2. A good definition of poetry,
3. how to read a poem.

I begin with a reflection on the difference between poetry and science, because they are often contrasted in a manner that implies discrimination against one or the other.  They are both essential to human life.  I feel very strongly about this, but you can skip the first part of the essay if it bores you.  It's about 40% of the way down.

Modes of thought: science and poetry
The scientific mode of thought is analytic.  Whether inductive or deductive, its certainties relate to matters of logic, including the logic of measurement and of math.  When the scientific mode is applied to the physical world, the information necessary to and resulting from that study is called "fact" and it is without emotional coloration.  We call facts objective, meaning that facts are entirely qualities of the objects we speak of, not qualities within ourselves.

The poetic mode of thought is intuitive and deals with metaphor.  A metaphor expresses our awareness of proportions and relationships which lie entirely within our perception.  When a poet says his sweetheart's cheek is like an apple, he is not only thinking of the generally round shape of an apple, but the delightful feel of an apple, the happy anticipation of enjoying it, and its sweetness.  He does not say her cheek is like a doorknob, as a computer might; but it is a round something which expresses freshness, ripeness and pleasure.  All this is complex to say, but it is immediate to human experience. 
Because such metaphors are based on interior experience (computers don't know about freshness), the poetic mode deals with matters which may have strong emotional color.  (My sweetheart!)  But even though these experiences are emotional and interior, they are still universal; they belong to human nature. 
And all language is built upon metaphor, not just poetic language.  The very word language is based on the Latin word for tongue.  The word "sad" originally meant heavy, because when you feel sad, it is like feeling tired from carrying a heavy weight.  Metaphors are everywhere.
The possibility of making metaphors flows from the uniquely human recognition of proportions which are clear to interior experience but which cannot be measured on the outside.  (How can you measure sadness?)  The general sensitivity to proportion is called Rationality, from the word ratio.  When we recognize measurable proportions, we can do science.  When we are sensitive to emotional and spiritual proportions, it is called Intuition.  The poetic mode of thought is intuitive.

Note on subjectivity
Intuitive insights are called subjective because they are experienced in the person (in the subject) who speaks of them.  Objective facts are within the objects we speak about.  But subjective matters aren't supposed to be irrelevant and thoughtless matters of emotional preference.  They can be very exact.  They just can't be measured with rulers.

Science and poetry
Natural Science is the orderly and consistent study of things which can be measured, weighed, or numbered, or whose relationships can be usefully expressed in equations.  Natural Science, supported by faith in a single and Fatherly Creator, comes to greater and greater clarity about the nature, properties, and construction of the material cosmos. 
Nevertheless, it must be understood that the idea behind a scientific experiment starts out as an intuition of an individual scientist.  The leap from the known to the unknown always starts out intuitively.  Therefore, although all science is analytic and experimental and can be tested by measurements, we still notice that Scientists (the real people) use both analytic and intuitive, modes of thought.  Besides that, the things scientists learn are often satisfying in their beauty as well as their clearness.
It does sometimes happen, alas, that the habit of measurement leads to the idea that measurement is the only way to be sure of anything.  Other operations of rationality are discounted.  In this diseased state, love of beauty and harmony may disappear from a person's life.  In such a state, a person may throw out poetry because it is "not scientific".  But in fact, the poetic and the scientific modes of thought are interdependent, natural, and everyday parts of human thought.  Their quarrel comes only when individual poets and scientists make fun of each other and try to cut each other out of life.  This has been a deepening cultural disease for several hundred years now, since Descartes.

But what is poetry?
Poetry is the most intense use of language, in which musical elements  meter, rhythm, rhyme, assonance -- give a kind of body to a thought which shifts the reader to a new level of consciousness.  The best prose and the best poetry share many elements of depth, beauty, and intensity.  But when the musical elements of language support the meaning of the words, those words definitely have the edge.  Why?  Because we humans live in the world with a body as well as a mind.  We like our thoughts to have bodies as well.
Poetic expression is not possible without patient interior attentiveness.  Although poetic metaphors cannot be checked with scales and rulers, they do follow logic, wisdom, and carefully observed interior and exterior experience. 
Therefore, poetry has precision.   Imprecision is not poetic.  Confusion is not poetic. Obscurity is not poetic.  Random words are not poetic.  The necessity of exactness is the reason we say that readers and writers of Poetry must use both the analytic mode [including dictionaries and diagrams] and the intuitive mode of thought.  If a poem seems obscure, figure out whether the obscurity is your confusion or the author's immaturity and silliness. It may mean something to deep to understand at the first reading; but it isn't poetry if it doesn't mean anything.
You see, a poet is a type of scientist, analyzing and working on the interior life.

Besides, all language is a web of metaphors.  Therefore, while science is directed to the organization of facts, and poetry to the portrayal of insights, they both depend on metaphor.  Metaphor builds upon facts and thought builds upon metaphor.  This is true for everyone.
Furthermore, as believers, and especially as Catholics, we know that the realm of invisible reality is an orderly realm, just as orderly as the realm of visible reality; therefore, some things are true and some false about the invisible.  So we want poetry to be about truth, just as we want science to be about truth.

How to read a poem

Now we can talk about reading poetry.

Learn the music
The first and obvious difference between prose and poetry is the music.  Poetry gives words a second form of body, not just the sounds of the letters, but the music of language.  There are several ways of making the music, several ways of encouraging the reader to hear and play it.  The most commonplace way is to give the words a beat -- a pattern of stressed and unstressed syllables, so many on each line.  Verses that were originally written to be sung often alternate one unstressed syllable with one accented syllable, perhaps four beats on the first line, three on the next, then four, and then three again.  Like this:

O beautiful for spacious skies
For amber waves of grain
For purple mountain majesties
Above the fruited plain

Can you see the alternation between stressed and unstressed syllables, just like the beat of the music?  Even without the notes of music, the beat of the words makes them easier to remember and more pleasant to hear.  Furthermore, the sense of rhythm and beat can be strengthened by making the ends of the lines rhyme.  When the rhyme pattern is perceived, the listener begins to expect the rhyme, and it gives a second cue to the end of the line.
Also, notice that in music, that last syllable often has a note with two beats.  When you read, consider giving some extra time to the last word in a line of poetry.  (I said consider.  It is not always the right way to express the thought.)
Another form of verbal music is alliteration, where the first letters of several words make the same sound -- "dim drums throbbing in the hills half heard" has two cycles of alliteration, the "d" sounds and the "h" sounds.  But even Jack and Jill going up the hill are alliterative.  It would be different if they were Zack and Jill.  When, as a reader, you find alliteration, be sure to give it enough breath so it can sink in.  That is your drama assignment.
Assonance is a third kind of verbal music.  In this case, it is the vowel sound that is repeated, not the consonants.  A green tree is assonant, or a red dress, or a tall awning.  Again, give it some breath and drama; don't just run past.  Stop a moment, pause in your reading, even just for a moment.
Now the reader has the potential of having four elements of music to incorporate into the drama of reading poetry: beat, rhyme, alliteration, and assonance.

Change of consciousness
A second quality of poetry is something profoundly human, a kind of miracle (or it may be called magic, since it is not necessarily religious) in which the heart is touched and the feelings shifted to a different interior space or to a deeper level of consciousness. It is this quality of the heart that marks poetry so that sometimes one notes a passage of prose and calls it poetry because it has such intensity.  "Beautiful prose" is close to poetry.  C.S. Lewis speaks of the line "Baldur the beautiful is dead, is dead," as the haunting line that really introduced him to poetry.  It caught his imagination.

Tennyson has a poem about elven bugles.  One verse closes with these lines:

Blow, bugle, blow, set the wild echoes flying
Answer, echoes, answer, dying, dying, dying.

This verse not only describes, but evokes the whole feeling for something that is wild and free and fleeting, something beautiful and rich that is slipping away out of reach.  Poetry takes us by the heart and brings tears to our eyes.  If you are not interested in being made to weep, consider that in the Middle Ages, the "gift of tears" was considered to be a gift of the Holy Spirit.  If you are of a more scientific bent, you might be interested to know that "wolf children" have been known to turn the corner towards human socialization when they first cry.  It is an essential part of being human.
For me, one of the lines that haunts my heart is from Gerard Manley Hopkins' "God's Grandeur":

And though the last lights off the black West went
Oh, morning, at the brown brink eastward, springs --
Because the Holy Ghost over the bent world broods
With warm breast and with ah ! bright wings.

I feel in these words the overwhelming sorrow and discouragement of human error and sin -- but then the heart leaps with encouragement, considering -- like a sunrise -- the bright and tender presence of the Spirit of God.
Whether it is tears or deep-shaken feelings without tears, poetry changes our consciousness.  The thing that people take drugs for -- the lift and startle of a consciousness profoundly drawn out of the ordinary -- is available to us in a pure and safe dose, for the enrichment of our humanity.  Better yet, in great poetry, this changed consciousness is unified with, rather than disjointed from, the fullness of human life.
It is because of this change of consciousness that poetry is always a drama, and must be read dramatically and without shyness.  You don't have to yell and flail your arms; I don't mean that.  But you have to give a body to the words.  Speak one line boldly, another in a whisper.  You are not reading the Periodic Table; feel the human weight of the words and convey that feeling.

Plain vanilla meaning
And yet, the matter of first importance in any sentence, prose or poetry, is its meaning.  In the reading of poetry, no pause or emphasis should by conjured up by a reader in such a way that it confuses the meaning of the words.  Coming to the end of a line of verse cannot be a reason to pause in a manner that disrupts the plain vanilla meaning of the text. This is where skill must be developed. 
First, consider that any sentence can be read a number of ways, each with a slightly different overtone of meaning.  For example, take the sentence: She went to the store.


1. If you say, "She went to the store," you mean that "she!" -- of all people! -- went to the store. 
2. If you say, "She went to the store," you mean that (after all that fuss) she actually went to the store, and didn't have to be driven or forced. 
3. If you say, "She went to the store," you mean she went right to it, without any side trips, without any confusion, just straight to the place. 
4. If you say, "She went to the store," you mean she went to the very store we were talking about so intensely, the one that figures so importantly in our present thoughts, the one and only, THE store that matters.
5. Finally, you might say, "She went to the store," meaning that she didn't go to the bus station, or to her friend's house, but, oddly enough, to the store.

All these readings are the same on one level: a girl went to a store.  But each has a different overtone.  It is this overtone that can be changed for dramatic reasons when you are reading verse.  When you read a poem, read it once for the meaning, ignoring where the lines end, attending strictly and exclusively to the punctuation until you are sure you know what it means.  Then go back and attend to the rhythm and rhyme, the alliteration and the assonance. 

Finally try to read it so that every grammatical point and every point of meaning is given its full due, and so that every rhythmic point gets its fair share without interference in the meaning, and so that the reader is invited into its heartfelt drama.  If you come to the end of a line of verse and there is no punctuation, see whether you can find a meaningful dramatic excuse for a momentary pause or emphasis.  You will usually be able to, but if you cannot, then you must read straight through.  To collect the music, the drama, and the grammatically correct meaning, and to do this naturally and without strain, is the skill of reading poetry.  It takes thought and it takes practice.

It is worth it
It is worth reading and learning poetry because it is worth having a store of words that evoke the inexpressible thoughts that we carry in our hearts. 
Rhymes are fun.  They introduce the idea of words having a body, a rhythm that is more than a symbol.
But rhymes are only the introduction to poetry.  They are like an alphabet.  If you don't enjoy rhymes, you won't be able to give poetry its body when you read it.  But beyond rhyme and that outward music, poetry is what makes language grow because it pushes the words for outward things into the service of deeper and deeper ideas.

What is Poetry?