Why do people write poems? There are a lot of ways to answer the question.
Here are the most popular versions.
A dialog of one is still a dialog. When you write for yourself, you may speak frankly. Instead of keeping your emotions bottled up, writing helps you deal with them.
Poetry absorbs sadness, disappointment, anger.
It beats depression. It heals.
Poetic devices let us express something that could not be easily expressed in analytical or logical forms.
We use non-standard сombinations of words to describe complicated individual experience. Literary images help us share important ideas - for example, about faith or social problems.
Having written some good poems, you can publish them in a magazine or recite them on a big stage. You also can become an author of a book to give it your acquaintances.
Oh, and the book is a possible source of income. It is nice to be reputable and rich, isn't it?
We write poems for someone in particular to please him or her.
For example, a poem is a good birthday present. Poems of this kind are often love verses. Rhymed declaration of love sounds well. It flatter the addressee's ego.
The person whom the poem is dedicated understands: “I evoked fervent feelings, I am charming.”
Dream of immortality
Sooner or later every person have to die. The fact frightens us, because we want to live forever.
Nowadays the only medicine for death is art. Great artists, sculptors, poets are immortal. They keep their senses and thoughts through creation.
You keep yourself in poems even if you are not a genius. Rhymed lines of a diary are better reminder about a person for his or her children than trivial family photos.
So in sum, any poems is really useful - at least for their authors. The literature is a blessing for readers too, but that's quite another topic.