"Bleeding" a brake system refers to driving all of the air out of the system. Modern automobile braking systems consist of a master cylinder in the engine compartment which pushes brake fluid (a hydraulic fluid mixture consisting primarily of various glycols) through a series of tubes (brake lines) which then actuate the brake cylinders. This is true whether you have disc brakes, drum brakes, or a combination of both.
The rotor is the "disc" in disc brakes. The rotor is gripped by the brake pads, which are moved (and held) by the caliper. This causes friction, which decelerates the vehicle.
Disc Brakes, invented during World War II for aviation purposes (especially the demand of landing on carriers and other short strips), are the most popular and effective way of providing braking force for automobiles, aircraft, and even other wheeled vehicles like bicycles. Disc brake systems are reliable, easy to maintain, and light in weight, especially when compared to drum brake systems.
The primary purpose of an automobile is to travel from place to place. However, you need (at minimum) some way to stop when you get there, and it is often convenient to have some way to stop while you are on the way there. This is where the brake system comes in.