Requesting help to understand this audio amplifier circuit
The arrangement of the 1M, 1k, variable resistor and 4.7 uF cap is a feedback circuit which determines the gain of the amplifier.

If we ignore the 4.7 uF capacitor for a moment and pretend that it is a short, the gain of the opamp + feedback is roughly equal to the ratio of the 1 M resistor divided by the sum of the other resistors. So here the gain will be between 1000 (variable resistor at smallest value) and 10 (100 k ohm variable resistor at largest value).

Now the 4.7 uF capacitor: its function is to block DC current so the resistance of the 1k ohm + variable resistor + 4.7 uF cap. will be infinite for DC. That means these 3 components are basically "not there" for DC.

So for DC only the 1 M feedback resistor is present and then the opamp is in a unity gain configuration meaning the gain is 1 (one) so no amplification at DC. This is useful as we're only interested only audio signals which are AC.

If at DC the opamp's gain is 1x, what then sets the DC voltage at input (and output since the DC gain is 1)? It is set by the 3.3M and 1M resistors at the input, they bias the input at about 1 Volt DC.

By not amplifying DC any DC offsets at the input of the opamp do not matter much. It makes the design easier and more robust.

To learn more about opamp based circuits read: Opamps for everyone which is a free Ebook from Texas Instruments.