I'm starting with the question of why people write poetry, rather than the question of what is poetry. In some ways I think that asking why is easier than trying to define what poetry is (which inevitably leads to debates about whether things should rhyme or not - stay tuned for next week on these and other exciting questions).
Reason 1: For yourself. Some people just write poems for themself - maybe because you feel sad, or angry or happy and you want to write a poem that no one else will see. I write these sorts of poems sometimes. For obvious reasons I am not going to post one here. I was going to put up a small sample, but quite frankly when you write for yourself its not the kind of thing you want splashed across the internet.
Reason 2: For someone in particular. Poems in this category are often love poems, or break up poems, and can end up really being for Reason 1, depending on how lame they are. The important thing is that they are just for that other person (or perhaps people).
Reason 3: For the world at large, in the belief that we all share exeriences in common. These could also be partially written for yourself, or for another person, but they also have something to say (or you think they do) about the human condition, life, love, death etc. Great love poems are usually written to someone in particular, but speak to many others of their loves.
Reason 4: For the world at large, to convince them of something. I guess you could call these political poems, or polemical poems, but I prefer not to. Here I mean that you have a view about the world - how it is, how it should be - and you write a poem to tell the world about it, and maybe convince them of something. Like poverty is bad, war is bad, destroy poetry.
Reason 5: For the world at large, because you want to be a poet. These are poems you write because you think other people will like them, and you will win the poetry slam, or get them published. This is the part of the poet that longs to be famous and immortal. This reason often shadows reasons 3 and 4. For some people it is an enemy, for some a friend.
There may be other reasons, but five seems like a good number. Below is a poem by John Donne, which I think it could be argued was written for reasons 2, 3, 4 and 5. This poem and many others by Donne can be found at http://www.luminarium.org/sevenlit/donne/.
by John Donne
MARK but this flea, and mark in this,
How little that which thou deniest me is ;
It suck'd me first, and now sucks thee,
And in this flea our two bloods mingled be.
Thou know'st that this cannot be said
A sin, nor shame, nor loss of maidenhead ;
Yet this enjoys before it woo,
And pamper'd swells with one blood made of two ;
And this, alas ! is more than we would do.
O stay, three lives in one flea spare,
Where we almost, yea, more than married are.
This flea is you and I, and this
Our marriage bed, and marriage temple is.
Though parents grudge, and you, we're met,
And cloister'd in these living walls of jet.
Though use make you apt to kill me,
Let not to that self-murder added be,
And sacrilege, three sins in killing three.
Cruel and sudden, hast thou since
Purpled thy nail in blood of innocence?
Wherein could this flea guilty be,
Except in that drop which it suck'd from thee?
Yet thou triumph'st, and say'st that thou
Find'st not thyself nor me the weaker now.
'Tis true ; then learn how false fears be ;
Just so much honour, when thou yield'st to me,
Will waste, as this flea's death took life from thee.