Would it help if I said this place was built in the early 50's? Don't think the electricity has been updated much since then.
A GFI is a Ground Fault Circuit breaker. since 1972, ALL "wet" (IOW, outdoor, such as a swimming pool, deck, or such and bathroom) installations were required to have them, in new installations OR when remodeling.
What they do, is to OPEN the circuit if there is a "fault" to the neutral or ground wire-- such as a defective appliance that would become dangerous and give one a shock, or a hair dryer tossed into a tub of water. In less than the blink of a eye, they will kill the power to the circuit, thus preventing electrocution of someone.
Nowdays, nearly ALL hair dryers, curling irons and other "wet use" appliances have a GFI built into the plug. you can identify these with the large plug that has a "reset" button on it. If one of these falls into a sink or tub, the power will be cut to the device immediately, and prevent the electrocution hazard.
In your case, perhaps if the breaker tripping is in the bathroom, maybe you have a GFI there. Otherwise, I suspect the hair dryer is wasted and presenting a short to the power source.