So the car slows down. The brake pedal is connected to a cylinder at each wheel by pipes containing brake fluid. Fluid is incompressible, so when force is applied to the pedal, that same force is transferred to each of the hydraulic cylinders and these push the friction material against the disc or drum.
There are basically only two types of brake operation: discs and drums. Drums are only found on the rear of some cars, because there are limitations to their efficiency. But for road use, their performance is generally acceptable, since they will only typically do 30-40 per cent of the actual braking work. The advantage, from a manufacturer's point of view, is that drums provide an easy way of allowing the hand brake to work, since a mechanical linkage can be easily incorporated into the basic operation.
There are four main aspects which will determine the amount of braking force that a system can generate:
The greater the diameter of the disc, the further from the centre of the wheel the braking force can be applied. This in turn will generate a greater braking force, or torque, on the disc. Remember that torque is a force applied at a radius to a rotational member.
However, there are limits to how big a disc you can fit, generally set by the size of the wheel. As a rough rule of thumb, 17" wheels can house a 343mm diameter disc, 18" can take 355mm discs and 19" can accommodate a 362mm diameter disc.
In addition to venting discs to allow additional surface area, some manufacturers drill through the disc from one face to the other. This is known as cross-drilling. The holes can lead to cracks forming in the material. But grooves on the friction surfaces of the discs tends to help cool the pad/disc area and prevent overheating, by carrying some air into that area, as well as removing debris such as brake dust.
It's the pads themselves that will have the biggest impact on the car's braking behaviour, since any pad will have an optimum range of working temperature. For example, on the road, you need a pad that will work immediately the first time you stomp on the pedal. However, the trade-off for that is that as you work the brakes hard, they will start to overheat and performance will suffer. The nightmare situation here is when the pads overheat and you get brake fade, where the brake pedal goes solid but no matter how hard you push, nothing happens. It's normally accompanied by a bad smell and smoke pouring from the wheels. Once they start to cool, they return to normal.
Cars that use their brakes really hard, like track day or race cars, will use a hotter compound of material. This will handle much higher temperatures without performance tailing off, but the range of temperatures it wants to operate at are higher. That's why you see racers left-foot braking as they do their warm-up lap, to get the brakes up to working temperature. On a road car, the first time you hit the anchors with race brakes, not much would happen.