"Is it wrong to offer an explanation for our poems?"
Wrong? No. But a poem should stand on is own, without gloss. As mentioned, I think we get a bit of wiggle room with the title. I've sometimes felt guilty for taking even that too far.
So, how important is it for you, as a poet, for people to understand your poem?
I want them to "get it". Understanding is a part. If a metaphor doesn't resound and an allusions is too arcane or specialized, then I failed. I already know what I'm going for. This is true for the structure, the sound, and the sense. It's not meaning alone that I'm trying to communicate, but I am certainly trying to communicate.
On the same token when you read poetry, how important is it for you to understand the poem?
Same boat here. I want to get what the poet was going for. that does not mean I can't appreciate elements in isolation, but I love it when a poem hits on all points and is musical, meaningful, and skillfully wrought.
And, if an explanation is either included originally or given later how do you feel about that?
I don't like it up front. It colors the initial read too much. I do enjoy it once I think I know the poem. But at that stage I would hope the conversation is akin to friends discussing an event they both experienced, or great movie they watched together. It shouldn't add to the poem itself. I just enjoy it.
Summing up, I don't think a poem should be accessible to everyone, but it should be accessible to someone. Otherwise, why bother.