When someone begins talking while you are already talking and interrupts you. The word can also be applied in situations where people are not supposed to talk i.e at an inappropriate time, during a moment of silence, or even during a movie.
The phrase comes from "jaywalking" when people who cross the street when they are not supposed to and interrupt the flow of traffic.
1. Dude would you quit jaytalking, I'm trying to tell a joke.
2. That guys a total jaytalker, he interrupts me every couple seconds.