The three major components of disc brakes are the rotor, the pads, and the caliper. The caliper covers a portion of the rotor and squeezes the pads against both sides like a vice. This has an advantage over drum brakes because the surface area that the pads contact, which is known as the swept area, is significantly larger. This means that it will remain cooler because the friction is being applied to a larger footprint. Additionally, the rotor is open to the air so it can be cooled by exposure to the atmosphere and the conductive cooling of air passing over it as the car moves.
Disc brake systems come in two styles: floating (or sliding) and fixed. Floating brake calipers have a piston on one side of the rotor and a bracket that reaches across to the pad on the opposite side. When the piston is powered, it pushes the pad it’s touching against the face of the rotor. Once that pad is in contact, the piston pushes the caliper back within the caliper bracket. This movement pulls the bracket on the opposite side of the rotor into the pad and, eventually, into contact with the opposite rotor face.
Fixed brake calipers are solidly mounted and do not move within their brackets. They will have a piston on both sides of the rotor, which makes them more expensive and complex. Some systems, such as those in high-end performance cars, will have multiple pistons on each side. To ensure even braking, the same number of pistons will be present on each side of the rotor so there will be an even number (4, 6, and 8. I’m not aware of anything larger than 8). These are either called 6-piston or 6-pot calipers.
Having multiple pistons allows for a more even distribution of force across the brake pad and for an increased total force applied to the pad. This can mean a greater normal force and increased friction. Increased friction will do a better job preventing rotation of the tire, but it’ll also increase wear on the rotor and pad. Multiple-piston calipers are larger so they typically accompany larger rotors. Larger rotors present a larger surface, which further increases the swept area, and helps to keep the material cool during intense braking.