Q1, D1, C1/C2, R3, L1 constitute a switchmode boost converter.
Q1 switches on, and current flows through L1. When Q1 switches off, the current decays via D1 and charges C1/C2. That's the boosted output voltage. I expect that the uC should have some way of sensing the voltage on C1/C2, probably via a resistive potential divider.