The brake master cylinder is where brake pressure is developed when the brake pedal is depressed. It then sends the fluid throughout the rest of the braking system creating hydraulic braking force. There are two chambers in the master cylinder and a fluid reservoir. If one chamber develops a leak, then the other chamber will act as a back up to keep the master cylinder functional.
The most common problem with the brake master cylinder is leakage. The seals within the master cylinder can develops a leak and allow brake fluid to escape. if a leak occurs, the the master cylinder will need replacing.
Most manufacturer factory warranties will cover the brake master cylinder under the bumper-to-bumper warranty section of the factory warranty. For extended coverage of the master cylinder after the factory warranty has expired, an extended auto warranty is an option. Certain coverage levels will include the brake master cylinder.