Function of Inductor in-line with MCU Vdd
It's to provide a low-noise supply to sensitive analogue parts of the MCU, such as PLLs or sometimes ADCs.

The supply rail will have a noise put on it by the simultaneous switching of lots of logic gates within the MCU. You may have other ICs nearby producing similar noise. The series inductor attenuates the noise conducted onto the analogue supply, the capacitors decouple it and attenuate the noise further by conducting it to the IC's 0V/GND.

It also stops noise generated by switching analogue circuitry, like PLLs, being conducted onto the supply rail.