The brakes of a car can catch fire for a variety of reasons, with the main causes being improper repairs and careless driving. Brakes can catch on fire when the driver is braking too hard, applying friction to the components within the braking system and consequently causing it to overheat, smoke, and even catch fire.
The build-up of dust on the pad carriers can cause the brake pads to stick to the disc. When this happens, the brakes can't return to their normal position and the wheel doesn't spin freely. The constant friction creates a lot of unnecessary heat which often results in a bad smell and sometimes smoke.