Twitter has been trying to buddy up with the TV industry for the past few years. Now it has its biggest payoff yet: A far-reaching deal with Comcast that aims to turn the social network into a TV-watching service. The gist: Later this fall, Twitter users will start to see a “See It” button on messages about some of Comcast-owned NBC Universal’s shows, like “The Voice.” Clicking on those Tweets will open up a Twitter “card” with more information about the shows, and Twitter users who are also Comcast pay-TV subscribers will be able to record or watch the show directly from their computer or mobile device. Even shorter gist: Twitter, which has been telling the TV business that it can deliver eyeballs to their programming, will now have a chance to prove it, by literally connecting its users with TV shows. “We want to make the conversation on Twitter lead to consumption,” says Sam Schwartz, Comcast’s chief business development officer.