This is a choke input filter.
The purpose of the (choke) inductor is to provide a stable current. This opposes any instability from VCC. If VCC is stable DC then AVCCInd will build up a magnetic field and let the DC pass. When there is a drop in current from VCC, the inductor discharges current from its magnetic field to keep the current at AVCC more stable.
The capacitor will oppose changes in voltage. If VCC were stable DC, then AVCC.c would charge to maximum capacity and then act as an open, allowing all the stable DC to flow to AVCC. If there is a drop in voltage at VCC, then the capacitor discharges its built up voltage into AVCC.
The inductor and capacitor work together to stabilize AVCC. Generally, the larger the values of the capacitor and incuctor are, the higher their maximum charge capacities will be, and AVCC will be more stable. If VCC is somewhat stable, and changes in current or voltage are brief and small, then lower values for the cap and inductor would be sufficient. If VCC is constantly pulsing at 60 hz or 120 hz, and changes in voltage and current are high (like after rectification of AC), then larger values for the inductor and capacitor would give better stability.