Why do we need to amplify the signal of an electret? I do understand from my reading that I should amplify the signal from an electret to be able to read it with an Arduino. I'd love to know the science behind that, why should we amplify the signal to be able to get a correct reading ?
Arduino (or any chip that uses ADC for that matter) has a resolution. For example, arduino analog read divides 5V to 1024 levels. A.k.a 0V -> 0, 5V->1024. That gives you 4.8mV per level.

Now assume that you want to read the voltage fluctuation of a very low voltage power supply that fluctuates from 0 mV to ~8mV. What does the arduino read? You'll see either 0 or 1. So basically, you just can't successfully read that low voltage with your current setup.

Now, if you use an analog OPAMP and amplify that signal to 5V, (0mV->0V, 8mV->5V) then you can use all 1024 levels available to you, provided by arduino.

That's why you need to amplify the signal.