The master brake cylinder, or more correctly, brake master cylinder, is one of five hydraulic fluid reservoirs and force transformers in your car’s brake system,. The brake master cylinder takes the input from the brake pedal, mechanical force, and transforms it into hydraulic force. This sends brake fluid through the brake lines to the four wheels of your car, where it is transformed back into mechanical force, to be used to stop or slow your vehicle. The master cylinder has a plunger in it that forces brake fluid through the lines to the wheel cylinders and calipers, to provide braking force.
For more info, see How to Tell if a Brake Caliper is Bad