Ok, I believe that you first used this microphone
that is not a real microphone until you scream on it. I am not sure but this microphone works only on half of the wave, it means that in silence it gives 0 and loud sound give 1023 on ADC. It is more like a sound sensor that can listen a hand clap, nothing more.
The remaining noise is due to the connections and Arduino itself but I was surprised about the quality of this simple recorder, I have a MAX 9814 microphone too.
Thanks for sharing your results!
Update: I made the same project and got the noise. I am using the laptop to power the Arduino and the laptop is connected to the mains. The noise came from the mains and the laptop.