Why place an inductor between Vin and Vdda (AVDD)
You are right, this is a filter - in particular, it is a lowpass LC filter. It is used on the analog supply to remove high frequency noise, which would impair the ADC's and/or DAC's accuracy. This is not need on the normal VDD supply lines, as the noise is less likely to impair the function.
Intuitively, an inductor's impedance rises with frequency, and a capacitor's impedance decreases with frequency, so only low frequencies can pass through this filter. High frequencies are shunted to ground.
Mathematically, the cutoff frequency is given by:
\$f_c = \frac{1}{2\pi \sqrt{LC}}\$
In the design given, the \$f \approx 30\ \mathrm{kHz}\$ so noise above that frequency, typically from an SMPS in this sort of system, will be attenuated. For an LC filter, the cost/size of the inductor usually constrains the design. The values here are fine to get started; if you were making 10,000 of the design you would think about whether it was needed, or if you could change to a cheaper RC filter, or smaller L etc.