I have to start with Raymond Carver, who has had the biggest influence on my poetry. At first it was the plain style, occasional humor and simple eloquence that struck me. It's taken awhile, but I think I've pinned it down - what precisely it is that draws me to his work and why I connect with it: his honest self-assessments and insight.
I'll be honest, the first piece of his which I read was "Your Dog Dies," which I wish I could quote, but I'm afraid to quote anyone as I am new to this media and am not 100% on what is allowed. Anyhow, I found it very funny,and mildly wicked. A better example of the quality listed above would be "Transformation" from A New Path to the Waterfall. (I don't have an underline button.)
Yusef Komunyakaa likewise demonstrates that kind of honesty, perspective and - what I admire greatly in his work -humility. I enjoy all of his work, but most of all his poems about his time in Vietnam. "Facing It," "Water Buffalo," and "You and I Are Disappearing" among others share an understanding of human weaknesses, fear and sadness without aspiring to grandiose statements.
The integrity and understanding of the poets Carver and Komunyakaa are what enable them to affect the reader or audience so profoundly. I believe, here, that you finish and do not gasp "Oh! What a well crafted poem!" or "How ingenious!" Instead you hear the last lines and gasp; you have an epiphany; you've gained something that is relevant to your own life.