The passenger brake is the nonexistant brake pedal located on the floor of the passenger (shotgun) side of the front seat of your car.
It is used instinctively by the passenger when the driver is driving insanely too fast, and the car needs to come quickly to a stop, which may not seem very possible at that particular moment.
It is sometimes used in conjunction with the OH SHIT handle by the passenger door.
Doris was using her passenger brake all the freaking way here. She's the one who made us late getting started from home by taking so long to get herself ready! I was just trying to make up some time getting through traffic...