How does one’s own experiences affect one’s interpretation of a poem?
Part of the beauty of poetry is that it is meant to be interpreted through our own reality, our own experiences. Most times, we have no way of knowing what the author was thinking or intending with each stanza, so how a particular poem relates to us as readers is completely up to us.
As humans, we naturally look for validation of our beliefs, and automatically try to relate the words and actions of others to what we have experienced in our lives. We also look for and respond to some things that are common experiences to all humans: love, grief, fear, etc.
So our own experience doesn't just affect our interpretation of a poem, it defines it, just as our experiences largely define us. In this way we can take from poetry those bits of relavance and understanding we want and need to, and Whitman, Bradstreet, Poe and others' works remain relavent for centuries.