C7 does not "amplify" anything. The gain comes from the op-amp, IC1B.
As others have observed, the addition of C7 into that feedback voltage divider means that AC signals will be attenuated by the voltage divider (R2/R8), and thus make the op-amp work harder to equalize the differential inputs. i.e. the opamp will AMPLIFY the AC signal.
However, at DC, there is no path to ground, so the opamp is limited to unity gain for DC signals. That is exactly what we want in an AC (audio) amplifier. We don't want any extra DC coming out of the output.
But note that there is ANOTHER function of C7 in this particular case.
Since this circuit has only a unipolar power supply, they are using that other voltage divider, R6/R7 to create an artificial ground for the opamp.
But since the voltage divider R2/R8 is connected to "real ground", that would create quite an offset in the output.
So C7 is also used to compensate for this difference in ground references.
You can calculate the value of C7 from the requirement of what the low frequency response of amplifier should be.
Roughly the 3dB down point is where the "reactance" of the capacitor equals 12K (R2 and R8 in series)
For example, a 0.5 uF capactor would make the gain of the amplifier roll off by 3dB at 26 Hz.
http://www.calculatoredge.com/enggcalc/Resistance-Frequency-Capacitance.htm