They've been working with ad agencies since April to develop a way to add targeted adverts in relevant comment threads while also making sure that the ads won't appear in a spot which would be detrimental to the brand image (think car insurance ad placed in the comment section following a traffic accident story).
The adverts will look something like this:
You can click on it to see an expanded view.
AdWeek reports that Disqus is working with Xaxis, an automated ad platform, to sell ad space to brands. The ads will be shown at the top of the discussion threads and marked sponsored. The ads will reportedly be optional (AdWeek says they're choosing not to exercise the option). There's also mention that publishers could share in the revenue.
While I don't like the idea of sponsored comments and see them as basically spam, I also know that this is not the first attempt Disqus has made at a business model. Disqus launched a premium VIP service in 2009, and I see mentions of it in 2010 but it seems to have been dropped some time in 2013.
I don't think there were enough sites willing to pay for the service. This is a problem faced by many startups that try to offer a freemium model, including Disqus's competitors like LiveFyre.