You already have some good answers, but another analogy I will throw out there is counting. If you are counting a large number of things while having a conversation on a different topic, sometimes you will lose your place. You can sometimes get away with a reasonable guess or quickly check some intermediate number you wrote down, but a lot of the time the easiest thing to do is simply start back at 1, as you know the way forward from there.
The reason why the same method works to fix computers, routers, TVs, and pretty much every other piece of electronics on the market today is that they almost all have computers in them. It’s cheaper to buy a mass-produced *microcontroller*, a.k.a. a small, low-power, single-chip computer designed to control things, than it would be to make custom control electronics.
As for why turning it on and off works, that’s because of it resets the program running on that computer back to the start. You can think of a program like a choose-your-own-adventure book. The pages, called *instructions* tell the processor to perform certain actions, like doing arithmetic, reading input, or sending output. If you give the program an input it wasn’t designed to handle, it can get stuck in a state where it can’t do anything useful, since the data in memory tells it whether or not to jump, and where to jump to. When you turn it off and back on again, you always get back to the first page, at which point it starts working again.
These devices run software. Software is a series of instructions. Sometimes the instructions say to do things that are impossible. The machine can’t do it, or follow any more instructions because it is stuck trying to do something it can’t do. Going back the start lets it begin running new instructions again.
A good example would be like if in a chess game you saw both of your bishops on the same colour squares. Something has gone wrong somehow. You can’t keep playing, and you can’t remember the moves that got you to this point. You simply have to start the game again.
The simplest way I can put this.
You know when you are typing your password into a website and forget one letter/number/symbol, then you delete the whole line and start again?
It’s kind of the same reason since computers can get stuck on code or have an unrecognised output and has to wait for the correct one. Turning it off and on again lets the device start from scratch again.
Anything that does this is a deterministic machine, which means every next state it will have is predetermined by the previous state and the input signals.
Sometimes the machine reaches a state in which the next one can’t be defined definitely. This is called an undefined state and is caused either by memory loss due to electric malfunction (static discharge or loose pins) or by improper implementation of the program e.g. the programmer missed a spot testing his code, or the state is forbidden and should be prevented by mechanical measures (e.g. the washing machine is filling with water while the door is open etc.)
A Reset forces the machine into a defined state (often the initial state).
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