The booster effectively takes the throw of your foot on the pedal and adds a bunch of force behind it, so the pedal moves easily and you don't really feel the strain of having to push a few liters of fluid through tiny lines around the car.
Think of it like a beer bong. If you just had a tube of beer and tried to drink it without using gravity (which is effectively a negative pressure sucking the beer into your gut from the bottom of the hose) you would be stuck drinking like you would out of a glass, but move it into a vertical plane and allow the pressure to do it's work, and you've got a beer in 2 seconds forcing it's way into your gut.
Manual brakes = normal drinking beer, takes time
Power Assisted Brakes = Beer Bong, instant beer