For me, writing is about communication: conveying the emotional state of the writer by recreating it in the mind of the reader. I value the way that good writing can sneak in under the most entrenched defences and unlock an emotional response.
I write poems because I love words - playing with them, building complex interconnected structures out of them, and most especially making music with them. The aural qualities of a poem are always important to me, and I'm only properly happy using a word if both its meaning and its sound are right.
I often use rhyme and strict forms; the artificial constraints they impose can actually free up the creative process and let the truth out. They're also good for provoking the delicious sense that you're not making something new so much as uncovering something that has always existed, word by tantalizing word.