What it does is allow you to leave comments after verifying yourself via any number of "log-ins" i.e. Facebook, Gmail, Ymail, etc. This lets YOU leave comments on my website all the while leaving me with the warm knowledge that you're a real person and not simply a spammer. It also encourages people to leave comments. Once you've visited once, your browser remembers and lets you be 'logged in' or 'verified' again.
Older posts on this site will have the Open comments of Drupal... but subsequent posts have the Disqus comment interface. One thing that I notice is that it embeds into each page seamlessly adopting the existing theme. Nice!