Simply put, this rule states that a person must listen to a conversation for 3 minutes before asking any questions. This allows the originators of the conversation to continue normally without having to reiterate points already covered and keeps the listener from looking like an idiot. It is invoked by the originators of a conversation should a third party ask a question which makes it clear that they haven't been listening.
Phil: So it turns out that tree in my backyard has a disease. We're gonna have to cut it down.
Jake: Oh yeah? That can get expensive.
Phil: Yeah, but I know a guy who knows a guy. College roommates. Now that I think about it, you've never met him. We should all get together and go bowling.
Jake: I love bowling. That reminds me-
Gary: Hey guys, what's up? Phil, did you ever find out about that tree?
Phil: 3 minute rule, Gary.