IRL it unlocks the throttle so that you can take it from the "idle" to the "stop" position.
Slightly different in the sim, as the idle/stop stop cannot be reproduced on our physical throttles.
Because you start the whole aircraft, not just the engine.
For example: only the start-up fuel pump is needed for starting up the engine. But then, when in flight with much more fuel flow, you'll need the main fuel pumps. Those need AC current, which is only provided by either the APU (if you got one) or the engine running alternators. That's why there is a third, specific fuel pump, runs on DC (= battery is enough) to be able to start when you don't have APU available.
After having shut-down other systems (BR, DA, D2M, LL, Radar and IIFF, INS, Sec ADI (caged + its power switch to the rear), ermergency hyd pump "EP", radioaltimeter, VTH, VTB, radios and lights):
- Throttle to STOP (use the little red round button)
- all 3 fuel pumps to OFF
- Fuel Cut Off to CLOSE (cover open/switch to the left side)
Then after engine has stopped:
- BATT switch to OFF.
That's not its name.
The fuel cut off valve does exist, it's a guarded switch in the start-up well "Coupe-Feu".