Why YSK: People seem to, on average, think that a car takes a lot of fuel to start up. In reality, it takes on the order of a few millilitres of fuel to start an engine. That means if your car isn’t equipped with an automatic start/stop system to stop your engine instead of idling, it saves fuel to turn off your engine and start it back up when you need it.
Caveat: air conditioning and radio might not work with the engine turned off.
Scenarios where this might be useful include waiting for trains to pass at rail crossings, waiting for food at drive-throughs, dropping off or picking people up on the side of the road when they need to load stuff, etc. May not be a good idea to use this while waiting at a red light because starting the engine does take time which would annoy drivers behind you when the light turns green.
Some cars are equipped with systems that will automatically stop the engine when you are idling for a while (e.g. waiting for a red light). If yours is, then manually turning off your engine will probably result in reduced fuel savings compared to just relying on the car to do it for you.
Regular old cars use weak starter motors from the 12V battery. They’ve gotten better, but it’s still just a small part used only to start the car, so it only turns over the engine fast enough to get it going.
A car like a Prius will put the car’s big, beefy generator in “reverse” to start the motor at whatever RPM the computer wants it at, and since it has abundant power from the synergy drive batteries, it can start the engine at whatever RPM the computer deems appropriate.