It’s sort of important to make the distinction between restarting a machine and physically unplugging / replugging it (known as power-cycling). Both can solve various problems which have been mentioned in the comments already.
For example, some Apple computers suffer from a bug where if certain USB devices are ejected (some USB hard drives, etc) the power delivery circuitry for that USB port may be turned off and may not be turned on again if you plug in another USB drive to the same port. But if you restart the computer the USB ports will reset and start sending power again.
Power-cycling can help by clearing corrupt data from a machine’s memory. The reason you must wait 10-30 seconds or however long is because it takes some time for electrical components such as capacitors to fully discharge. You can see this in action when you unplug some laptop power supplies and their power status lights remain lit for several seconds after the power is unplugged. If you don’t wait long enough and the capacitors haven’t fully discharged then you may simply be performing a hard reboot rather than a proper power-cycle.
Best way I’ve had it explained is as follows:
You know your way from your home to the shop, but you accidentally take a wrong turn and continue to try to correct it but now you’re lost and have no idea how to get to the shop, or how to get home.
If someone were able to put you back home, assuming nothing goes wrong you should now know the way to the shop again from here.
Turning off the computer puts it back home so it knows the way to the shop again.
Someone posted a great response a while back.
“You’re travelling through an unfamiliar neighborhood, you keep making left and right turns but nothing is familiar so you just keep on going and going. Turning on and off puts you right at the entrance of said neighborhood, now you know which turns to take.”
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