Mic level, line level, and instrument level refer to the voltage level of mic, line and instrument signals, and also to their impedance, or current-delivering capability. Why do these differences exist?
"For historical reasons" is the answer to a great many questions, inside and outside of audio. Things happened in the past that led to things being the way they are today. Like the British habit of driving on the left side of the road, which apparently stems from horse riders wanting to have their sword hand free to tackle potentially aggressive approachers. Well that's one theory.
So for various historical reasons microphones have a low output level of somewhere around 10 millivolts or so, varying of course with the loudness of the sound source and the distance of the mic from the source. They also have a lowish output impedance, typically around 200 ohms, which means they can supply quite a strong electrical current.
Line level, again going back to history, derives from 1 milliwatt of power traveling through a telephone cable with a characteristic impedance of 600 ohms. Using Ohm's law we can derive a voltage of 0.775 volts. So the level of a line output is around 0.775 volts, or you can say around a volt because we don't need to be that precise. Line level outputs are always powered so the impedance can be low, and by low we would consider anything less than about 150 ohms, and it could be a lot less. Low impedance again leads to high current delivery capability.
What about instruments? Well we can think of the electric guitar with normal passive pickups. We can see from this interesting table that an electric guitar can pump out around 150 millivolts from the strum of an E chord. That's not a bad voltage but you have to consider that it is only the energy supplied by the player that is converted to electricity. There is no other energy input. So to achieve that fairly high voltage of 150 mV, the consequence is that the output impedance is high, around 5000 to 10,000 ohms, rising further towards higher frequencies. This means that the capability to supply current is not good and significantly worse at higher frequencies.
I could delve further into the electronic math, but it's more interesting to explore the consequences of mis-connecting...
I could go through the other possibilities but I think you should get the gist by now. Microphones, line level sources, and instruments should each be connected to the proper input.
Oh, I didn't mention that many microphones need phantom power. You won't get that from a line or instrument input so the mic won't work at all.
And... If you connect anything but a microphone to a mic input that has 48 volts phantom power... Well you may get away with it but don't blame me if your 1959 vintage Les Paul Standard gets its pickups blown.
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