Inside the booster there is a diaphragm. On one side (the side that faces the brake master) you have engine vacuum. On the either, you have either engine vacuum (when the brake pedal is travelling upwards), or ambient air (when the brake pedal is travelling downwards).
When you press on the pedal, you press a poppet valve that isolates the two halves of the diaphragm from each other, and at the same time allows air in via an intake (it's what the black plastic piece around the pushrod on the cabin side is covering).
When the pedal starts moving upwards as you release the brakes, the poppet valve isolates the booster from ambient air and joins the two halves of the diaphragm, allowing the air in the booster to be evacuated into the engine intake.
Applied force would be area of the diaphragm multiplied by the pressure differential. It would be a lot, I reckon well over 100kg for most passenger cars.
I think the key concept behind the booster is that it provides assistance as a function of the brake pedal's acceleration, and how hard you are pressing on the pedal rather than as a function of the absolute position of the pedal in its range of motion. It doesn't multiply braking force quite the same way lever ratios do.
