The most common cause of smoking brakes in a car is friction. The friction can come about because the parking brake is left on, the brakes are working especially hard or because the brakes were recently replaced.
According to the CarsDirect website, brakes often start smoking or emitting a burning smell when the driver is riding the brakes, especially down a steep hill. This also happens when the car is driven with the hand brake left engaged.
According to O'Reilly Auto Parts, smoking brakes can be symptomatic of several problems. For one, dirt and debris may have worked into the brake system. Smoke results when the foreign material gets caught in the braking mechanism. Sometimes getting the brakes serviced or replaced causes the smoke. Contaminants from the service may settle on the surface of the rotors and get burned off during use. Another problem might be that the calipers have gotten stuck. The calipers are supposed to clamp the rotors and brake pads together when engaged, but they can become stuck and create constant friction. Drum brakes and wheel cylinders can also become stuck. The resulting friction sometimes causes smoke.
In the case of debris or contaminants from a service, cleaning the brakes should fix the problem. However, if parts of the brakes are stuck, service is necessary to fix the problem.