Non inverting op-amp resistors
R1 and R2 mix the input signals and the POT acts as volume control, attenuating the input using a voltage divider. R3 makes the volume control response non-linear, which is desirable in this application.

The inputs of the LM324 can reach 0V, due to their configuration. Such low common mode voltage is not a problem in this case but the lack of AC coupling is strange.





This is the effect of different values of R3 (the x axis is the POT position):



Update After viewing the video you posted on the comment it's clear now that the circuit doesn't have an audio output. If the input doesn't have a DC bias, the amplifier is just clipping the negative parts of the signal, which makes no difference for the LED Sign VU meter. Previously you had just mentioned that you "came across this schematic".

The ear responds to the loudness of sound logarithmically (http://physics.bu.edu/~duffy/py105/Sound.html). If the volume control is linear, it "feels" like not being effective in higher amplitudes.

A different way to achieve the non-linearity is using specific pots: Why should I use a logarithmic pot for audio applications?. But, in the circuit you mention, a linear pot will form a voltage divider in which the lower part is in parallel with R3, which gives you a non linear equation with respect to the pot position.