In reference to Grey's Anatomy; refers to the act of connecting sexually or romantically with a close friend (often who has sexual/romantic feelings towards you) which you have no sexual or romantic feelings towards. Often occurs due to loneliness/horniness or confusion.
This act will usually be followed by an immediate negative reaction from the "Meredith", after realising that they have made a mistake.
Joe: Did you hear that Sara hooked up with Zak at the party on Saturday?
Bob: No way! I thought she liked James? I mean, I knew Zak liked her...
Tim: Didn't she bail right after though?
Joe: Yeah, she was just pulling a Meredith.