OK I'll start and then others can chip in and expand and/or correct as necessary.
Your Master Cylinder is connected to the brake pedal. The servo is a vacuum operated device that magnifies your foot pressure, and so increases braking efficiency.
The Slave Cylinders are the brake calipers. There's one attached to each wheel.
When you press on the brake pedal, hydraulic fluid is pushed from the master cylinder along the brake lines into the slave cylinders. The pistons in the slave cylinders are pushed out of their housings by this fluid, so pressing into the backs of the brake pads and squeezing the brake disk betwee the pads. Thus, hopefully, slowing the car down.