The brake booster assists braking power by adding extra force via vacuum from the engine to the hydraulic part of the brake system. If you didn't have a brake booster, the brake pedal would be tough to push and stop the car.
If you have ever driven an older car from back in the sixties, you would know what I mean because older cars didn't have brake boosters. If you would like to know what it feels like to not have a brake booster, turn off your car while it's in park and press the brake pedal four times, on the fourth push you will have used up all the stored vacuum in the booster, and the brake pedal will become very hard.
The brake booster is usually found between the brake master cylinder and the firewall; it looks like a big black metal doughnut.