"Battery Brain" is an electronic device that acts as an ON/OFF switch between your car battery and the car's electrical system. If your car has some kind of problem with it's electrical system, or if there is a condition present (such as leaving the car's headlights or interior lights on or anything that may accidentally drain the battery), the "Brain" that is attached to the car battery will disconnect the load when it's power charges reaches a certain level. That way, it prevents the car battery from being totally drained.
The "Battery Brain" will not disconnect the load from the car battery while the engine is in normal operation. (Manual reconnection under the bonnet, remote connection as well as manual and remote disconnection acting as an anti-theft device).