We have the brake pedal, the push, rod, the servo, the master, cylinder, the reservoir and hydraulic lines. The brake pedal transfers the mechanical force applied by the driver to the push rod the push, rod, transfers the mechanical force applied by the brake pedal through the servo to the master cylinder, the brake, servo or vacuum booster assist the driver by applying additional force to the Braking system the master cylinder converts non hydraulic pressure from the drivers foot on the brake pedal into hydraulic pressure when braking pistons with seals and springs in the master cylinder create hydraulic force which pressurizes the entire hydraulic system. Brake fluid returns to the master cylinder. When pressure is released, the reservoir holds sufficient brake fluid to stop air getting into the hydraulic system. Finally, we have the hydraulic lines which carry the brake fluid to the front and rear brakes now lets take a look at the hydraulic system in action. Here we can see the wheels turning pressing the brake pedal, extends a push rod through the brake servo and into the master cylinder the master, cylinder pressurizes, the entire hydraulic system and forces brake fluid through the hydraulic lines. Releasing the brake pedal reverses the process. The hydraulic pressure on the entire brake system is reduced, allowing brake fluid to return to the master cylinder. A combination of seals in the caliper and springs in the brake drum then return the brakes to their original position, allowing the wheels to turn freely once more brake.

Fluid travels through the hydraulic lines, applying pressure to the caliper or wheel, cylinder pistons, which in turn create the friction force required to slow the wheels and thats the basics of how a hydraulic brake system works.

https://www.youtube.com/watch?v=zbtwOedDMlM