Someone who can easily run a conversation, like a quarterback runs an offense. Will make you either easy to talk to, or just make people want to punch you in the face.
Jen: I don't think I can go out with Steve, I'm too shy to talk.
Beth: Don't worry, he's such a conversation quarterback, he'll make it easy for you.
Dude: Man, fuck Brent! He's such a conversation quarterback that he won't let you get a word!