Can someone explain this microcontroller ADC interface (for reading solar panel voltage)?
What is the role of the pnp transistor network?




It's a differential voltage to current converter followed by a load (R34 and R35). The voltage between P+ and P- sets a voltage across R31. This (minus 0.7 volts) sets a voltage across R33 and that causes a current to flow out of the collector (largely irrespective of what load the collector has).

Given the values of R33, R34 and R35, whatever voltage is set across R33 appears across R35 but, reduced by 3:1. 

Importantly, this voltage is ground referenced making it suitable for the ADC to make sense of. So there is level shifting involved.