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.
Acquaintance of my dad’s was seriously injured a few decades ago when he was rear-ended at a stoplight. It was by a car that had its brakes out and had slammed into the back of his car. It’s a pretty rare chance, but to be fair the person above you is talking about non-zero chances here.
Similar thing also (allegedly) happened to my driving instructor when I was in driving school except it was an 18-wheeler. He had the reaction time to drive out of the way and into the other lane. If his engine were off he likely would have died due to the time it would have taken to start it. I don’t know how real that one is though, it was a story he told all the time.