When the brake pedal is pressed, the piston of the master cylinder applies pressure on the brake fluid.
This pressure is transmitted uniformly to each cylinder at the wheel, cause the pistons at the wheels to push the brake shoes to press against the surface of the brake.
The friction between the brakes and brake shoes causes the vehicle to slow down and stop.

Q: Why is it dangerous if air bubble is trapped in the brake fluid of a braking system.

A:

If the air bubble is present in the fluid, the fluid becomes compressible.
This may prevent pressure transmits through the fluid and hence causing an ineffective braking effect.

Q: Why oil but not water is used as the hydraulic fluid in a hydraulic brake system?

A:

Because the boiling point of the oil is much higher than water. This can prevent the hydraulic fluid from boiling when the brake is very hot.
Water may cause rusting in the part of the braking system

When the handle is pressed down, valve A is closed whereas valve B is opened. The hydraulic fluid is forced into the large cylinder and hence pushes the piston moving upward.
When the handle is raised, valve B will be closed while vale A will be opened. Hydraulic fluid from the buffer tank will be sucked into the small cylinder.
This process is repeated until the load is sufficiently lifted up.
The large piston can be lowered down by releasing the hydraulic fluid back to the buffer tank through the release valve.