HI.
The circuit basically is a differential amplifier with high frequency filtering (C9, C11, C3 and C12). The half voltage (Vcc/2) is necessary since the input goes through a dc blocking capacitor (on all 4 input signals) so you get both positive and negative voltages at IN+ and IN- and the Op-Amp is just powered from 5V to GND. The resistors divide the voltage and the 4.7uF (relatively large) capacitor acts as a voltage source so the op-amp output would be half Vcc for no (0V differential) input. The small (33pF) capacitors allow high frequencies to be effectively grounded before reaching the Op-amps inputs (either to the Vcc/2 source or Op-amp output which acts as a V source). Then the output is also dc decoupled.
Without the Vcc/2 bias the op-amp would cut off the negative part of the signal like a diode passing an AC signal.