Recently I seem to be receiving quite a lot of questions regarding brakes and through the series of questions, a rather acceptable explanation surfaced. So I'm here today to share what I'd come up with in the past few days.
In a simple explanation and disregarding all hydraulic circuits. A brake system consists of 3 parts, the caliper, the rotor and the brake pads.
Let's start with the simplest component - the brake pads is a body of friction material glued together with a strong adhesive. Its (brake pads) main function is to provide friction when it comes in contact with the brake rotors.
The caliper is a clamp which forces the brake pads together to transfer kinetic energy to heat energy through friction, and the pots referred to in the braking system are the pistons found in the calipers. The more "pots" (pistons) you have, the more evenly distributed the brake force will be (improving brake pad wear).
The brake rotors are essentially round metal (or other material) plates attached to the cars knuckle to provide a friction surface and a simple mechanism for braking loads to take place. The brake rotors are also known as discs (due to their shape). Since the rotor's function is to stop the car by means of energy dispersion, it can be reasoned that, the larger the discs the better.
"Why?", you ask. The larger the disc, the more heat capacitance the rotors can take and the more surface area exposed to air cooling it can provide. Although, modern day, albeit exotic materials are slowly being introduced to make the rotors more facilitating to heat and its effects (warping and cracking).
Another function of the rotor, as I've mentioned above, is to provide a simple mechanism for braking loads to take place. This simple machine acts on the Law of Moment, whereby, M=Fd (M-Moment, F-Force, d-distance). To put this machine into perspective, let's assume all forces acting upon the system are specific points. The mounting point of the rotor will act as the fulcrum, the diameter from the mounting point until the brake pad engagement area will act as the length, and the brake pad engagement area will be the point where the force acts upon this mechanism. With respect to the equation for the Law of Moment, it is seen that the diameter of the rotor (d) is inversely proportional to the amount of force (F) is needed to achieve the same moment. In laymen's terms, the larger the rotor, the less force will be needed to achieve the same amount of braking.
From the explanation above, the larger the disc, the more powerful this effect will be.