The brake booster works by using the engine's natural vacuum in the intake manifold to exert suction on the master cylinder side of the diaphragm when you step on the brakes. This assists your foot pressure on the brake pedal to give you additional braking force. When you release the brakes, the pressure equalizes on both sides of the booster. It's a simple and effective system.
But the diaphragm in the booster breaks down eventually - especially if your brake master cylinder is leaky and deposits brake fluid in the booster body. When the diaphragm finally rips or develops a hole, you lose the vacuum boost to your braking, but there's also a more insidious problem - when the diaphragm no longer holds vacuum, every time you step on your brakes you're allowing air to rush into your intake manifold, changing the fuel-air mixture your engine needs. What's worse is that in Chevy small block designs, all the vacuum used by the brake booster is drawn from the #1 cylinder runner. This means that every time you step on the brakes, you're creating a super-lean running condition in that cylinder, and that will shortly lead to detonation (pinging) and potentially damage to the #1 cylinder that will require an engine rebuild or replacement.
You can tell when your brake booster is dead because your brake feel will change. You may also hear a "whoosh" sound when you step on the brake pedal. You can do an easy test to make sure the booster is working by stepping on the brake with the engine off. The pedal should feel firm. Now start the engine and if the pedal drops an inch or so as the engine starts, your booster is in good shape! But if your booster isn't boosting any more, replacing it is easy. Just follow the steps in this article.
We used our About.com Project Corvette for this job, because it needed the work done! The photos and instructions are correct for a 1977 Corvette, but you should always use a proper repair manual for your year and model of Corvette.