The brake booster, or power assist, is normally located behind the master cylinder. Many operate by using engine vacuum and a diaphragm to help assist in brake application.
If your brake booster fails, you often have a very hard brake pedal. You might still be able to stop the vehicle, but it will require a great deal of effort to do so. The first thing to check is the vacuum line going to the booster. Next, inspect the check valve that might be located in the vacuum line somewhere. Sometimes they're part of the feed line and cannot be accessed externally. If this type of check valve goes bad, you replace the entire vacuum hose. This check valve allows vacuum to go to the booster, but not back to the engine. When brake boosters fail, it's often a result of a master cylinder failure. Sometimes when a master cylinder fails, it leaks fluid into the brake booster. This can sometimes eat through the rubber diaphragm in the booster and cause it to fail. Other times, I've seen the return spring in the booster break and rip the diaphragm. Sometimes you can hear a hissing noise under the dash when a brake booster fails. This is the vacuum escaping. This vacuum loss can also cause engine performance issues. Either way, the fix is the same: Replace the brake booster.