Yes, Huffington Post would post my comments to their news articles and blogs to my account, so anyone that views my profile (or perhaps my blog) would see my comments made. I'm not sure how it's going to work, which is why I'm allowing it. Huffington Post is a site I trust. I have my Tumblr, Facebook, and Twitter accounts connected (so I can choose when I want certain comments posted to those sites), and would like to do the same with WordPress.
I'm not sure exactly what they mean by Host. Could it just be that they want the website address? I'm not sure...