We give site owners a hassle-free discussion platform that can be integrated into their websites with additional perks such as moderation tools, analytics, spam filters (trained on the whole network of websites and not just one) and others.
And people leaving comments on different websites are now able to manage and control their comments across the web, and use their Twitter/Facebook/Google accounts knowing that Disqus will never abuse their trust. Boxed software installed on different sites managed by different people would likely never be able to provide neither the integration nor the trust.
But don't get me wrong, we absolutely love open source. Check out our Code page[1] or our public account on GitHub[2]. We released many different projects, some of which are adored by the Python/Django community (e.g. Django Sentry). I think Disqus as a product is better when it is a service and not a boxed software.
Anton
[1] — http://code.disqus.com/code/ [2] — https://github.com/disqus/