The 3.3V reference for the first op-amp IC1 is used to create a 2.5V offset, so the AC voltage centered at 0v ± 2.5V is converted to a voltage centered at 2.5V ± 2.5V, i.e. a range of 0-5V since the TLC2272 is a single supply op-amp, and can't generate a negative voltage from the negative half-cycle of the input.
As the description says, "Resistor R2 adds a dc offset current to allow for both polarities in VIN."
The top LED in IC2 is lit during the positive half of the cycle, and the bottom LED is lit during the negative half.
The two pots connected to IC3 are used to adjust the gain and provide an offset so the AC voltage centered at 2.5V ± 2.5V with a range of 0-5V.
Note the description in the second paragraph says, "Variable resistor VR2 trims the overall gain, and VR1 adjusts the output-voltage offset, which is nominally 2.5V."
I agree with Kevin that it's not obvious why the second 3.3V regulator is really needed, unless the designer is trying to keep the reference separate from the supply to the op-amps. But then they are using 5V to bias pin 2 of IC2.
It's also odd (IMO) that there are no bypass caps (e.g. 0.1 µF) shown for either op-amp supply. I always use bypass caps on any IC, whether digital of analog.