How does this LM386 circuit boost bass?
Think of it this way, at low frequencies, the external series RC network is effectively an open circuit so the amplifier behaves as if the network were not present.

At high frequencies, the RC network is effectively just the 10k resistance.

Looking at the equivalent schematic in the data sheet, note that this 10k resistance is in parallel with the internal 15k feedback resistor.

So, instead of a 15k feedback resistor, there is, at high frequencies, effectively just a 6k resistor , i.e., there is more feedback at high frequencies and thus, reduced gain.

In fact, rather than boosting the gain at low frequencies, the addition of the RC network actually reduces the gain at high frequencies.  The effect on frequency response is equivalent; the bass frequencies are amplified more than the high frequencies.