Think of why people choose to write poetry and the different styles it is written.
Emily Dickinson once said that you know good poetry when you read it because "it takes off the top of your head". I think good poetry works its magic on everyone that way...it's good to you at the moment because of the certain set of circumstances you're dealing with when you read it. It speaks to you and hums with meaning...you "get it" and it gets in you. It's a series of good words chosen to represent the good ideas about ordinary topics in an extraordinary way.
Poetry comes in so many different styles because it's written when people are particularly passionate about a topic. People are as different as the moods and feelings they experience...as different as the way they express those feelings...as different as the many forms of poetry which serve as the vehicle of that expression. The format they choose is the one that fits that topic, that current event, that feeling, and maybe most importantly, the poet's personality and style. Sonnets, lyric poetry, dirges, hiakus...they are chosen for the feeling and the purpose of the author as much as they are chosen for the topic. It's art, and it's not so different from the paintings in a artist's "blue period" or "retro period". People go through moods, peaks and valleys, hard times and gloriously wonderful times...the poetry illustrates it all.
Its interesting that the first thing that came to my mind when I read the question was the smell of fresh, pink roses: My favorite flower.
I then imagine that I relate that to my personal meaning of poetry: Poetry is the muse that moves your thoughts to everything that is exquisite, and everything that makes you want to experience the most intense sensations.
What I love about poetry is that it is stripped down to the absolute essense of a thought or feeling. Far more than prose, it can be startling, inspiring, shocking, etc.
As for writing, poetry is challenging to write but very rewarding. It forces you to decide exactly what you want to say, and to say it using only the perfect words. I feel that writing poetry makes me a better writer of prose as well.
Coleridge said that poetry is the "best words in the best order." What makes great poetry is the lasting impression it leaves you and if you think of the poem often when in similar situations as the narrator. Not everyone loves all poetry, and some poetry is extremely difficult and ambiguous.
People choose to write poetry because they have a theme, and they have the right words to express that theme.