It integrates Twitter accounts into your website. When users click a link, they can follow your writer, see her latest tweet, etc on your site. This information is provided by small modal overlay popups. This is an obvious value-add for content/media websites. Twitter is launching with 10,000 sites including NY Times, Huffington Post
From the Twitter blog:
When we designed Twitter, we took a different approach—we didn’t require a relationship model like that of a social network. Keeping things open meant you could browse our site to read tweets from friends, celebrities, companies, media outlets, fictional characters, and more. You could follow any account and be followed by any account. As a result, companies started interacting with customers, celebrities connected with fans, governments became more transparent, and people started discovering and sharing information in a new, participatory manner.
Later in the interview, Evan was asked what he thought about his company, with regards for openness. Evan responded by saying that they had a lot of discussions at Twitter of whether to use the word 'open' or 'transparency'. His conclusion was that, "A window is transparent but a door is open." He said that they always try to proceed down the road of openness. We have of course seen this with how 3rd party developers are able to use the versatile Twitter API to use twitter in many ways, from 3rd party apps to social media mashups with other services, such as Foursquare or Gowalla.