send and recieve analog data from one arduino to another arduino via web/ethernet
ADC input has 100Mohm impedance. By placing C4 the signal at the ADC input has no DC path, is just floating between -0.7v and 5.7v , limited only by the input clamping diodes.
ADC can convert only voltages between 0 and the voltage reference, I suppose you use the default 5V reference.
But your signal is floating, and the ADC will cut any peaks outside of the conversion area giving the noise you hear.
Another issue I see here is that the data sheet of LM386 specifies a load between 4ohm and 32ohm. There is no warrantee that it will work without a load as in your case. Most likely not.
So you might want to connect C4 to a proper load and take the signal for ADC straight from pin 5 of LM386 which is auto balanced at half of the voltage supply.



simulate this circuit &ndash; Schematic created using CircuitLab
Later edit after I found the source of the schematic, there are also comments there that the schematic will never work with Arduino with the capacitor connected, the only working application was a sound detector where the signal distortion does not matter.
Please do not trust the content of any unknown website published by an anonymous just because it looks like a tutorial made by somebody who knows something.
Edit to add some info on how to debug the issue.
First, in the above schematic replace the resistor with a speaker and see if the sound is good. If not than see what is wrong with your amplifier.
If it's good and loud without any distortion then put the resistor back.
Use a binary mode serial monitor like Realterm to see how your data looks, the Arduino serial monitor works only in Ascii mode which turns a byte into three ascii chars which is slow.
Something like that
void setup() {
    Serial.begin(230400); // opens serial port, sets data rate to or maximum supported by your board to minimize latency
}

void loop()
   {
     unsigned int temp;
     temp = analogRead(0);
     temp = temp&gt;&gt;4; //strip low bits to fit in a single byte
     Serial.write(temp);
   }

Then see how your data looks, if you have to many 00 or to many FF than you know that your data us upper or lower limited or what is wrong with your signal.
I hope you are aware that the ADC conversion takes 100us and the wire transmission also around 200us the maximum sample rate you can expect is around 3khz and a maximum bandwidth of the audio signal of 1.5kHz which is half of the telephony bandwidth, you might want to use a faster DAC and use some non blocking ADC reading to use the time while ADC is working like in this article