A compressor bypass valve (CBV), also known as a compressor relief valve or diverter valve, is a vacuum-actuated valve designed to release pressure in the intake system of a turbocharged or centrifugally supercharged car when the throttle is lifted or closed. This air pressure is re-circulated back into the non-pressurized end of the intake (before the turbo) but after the mass airflow sensor.
A blowoff valve, (BOV, sometimes hooter valve, not to be confused with a dump valve) does basically the same thing, but releases the air to the atmosphere. This creates a very distinctive sound desired by many who own turbocharged sports cars. Some blowoff valves are sold with trumpet shaped exits that amplify the hissing sound, as not all blowoff valves are the same, some make different noises and these designs are normally marketed towards the tuner crowd. For some owners this is the only reason to get a blowoff valve. Motor sports governed by the FIA have made it illegal to vent unmuffled blowoff valves to the atmosphere. In the United States, Australia and parts of Europe cars featuring unmuffled blowoff valves are illegal for street use.
The unique sound caused by a blowoff valve (but not a compressor bypass valve) sometimes comes at a price. On a car where the blowoff valve is mounted after the mass airflow sensor, venting to atmosphere confuses the engine control unit (ECU) of the car. The ECU is told it has a specific amount of air in the intake system, and injects fuel accordingly. The amount of air released by the blowoff valve is not taken into consideration and the engine runs rich for a period of time. Engines with a manifold absolute pressure regulated ECU or where the blowoff is mounted upstream of the MAF sensor are not affected.
Typically this isn't a major issue, but sometimes it can lead to hesitation or stalling of the engine when the throttle is closed. This situation worsens with higher boost pressures. Eventually this can foul spark plugs and destroy the catalytic converter (when running rich, not all the fuel is properly burned in the cylinder which can allow unburned fuel to combust upon contact with and melt the converter or to cause incompletely combusted fuel to leave heavy carbon deposits).
One way to correct this problem is to reduce the boost going into your engine. This will cause the piston in the blow off valve to only open slightly. Another way to correct this problem would be to plumb the MAS after the BOV. You could also recirculate the air back into the intake, which is the stock setup for cars with a downstream MAF sensor.
The dumpvalve also releases air into the atmosphere. A BOV is a type of dumpvalve.
Blowoff valves are used to prevent compressor surge. Compressor surge is a phenomenon that occurs when lifting off the throttle of a turbocharged car (with a non-existent or faulty bypass valve). When the throttle plate on a turbocharged engine running boost closes, high pressure in the intake system has nowhere to go. It is forced to travel back to the turbocharger in the form of a pressure wave. This results in the wheel rapidly decreasing speed and stalling. The driver will notice a fluttering air sound.
A blow-off-valve is connected by a vacuum hose to the intake manifold after the throttle plate. When the throttle is closed, manifold vacuum without pressure develops in the intake manifold after the throttle plate and "sucks" the blow off valve open. The excess pressure from the turbocharger is vented into the atmosphere or recirculated into the intake upstream of the compressor inlet.