The braking system of a car is a series of levers. Some are mechanical (pedals and brake shoes for instance), others are hydraulic.
Small bore master cylinder operating large bore slave cylinder = more pedal travel = more leverage. Think of the the diameter ratio between master and slave like a lever ratio. A 10mm master cylinder driving a 20mm slave cylinder gives a 2:1 leverage - same effect as putting the fulcrum 1/3 the way along a lever.
