When analog and digital circuits coexist on the same power supply and ground nets, there is a possibility of crosstalk: digital circuitry has sharp edges and current spikes which can be seen on the supply voltage degrade the performance of the analog section.
By separating the two grounds and power nets, the connection may be made at one appropriate point. When the designer also pays proper attention during circuit board layout, such crosstalk can be minimized.
As for the inductor symbol, it's actually a ferrite bead which passes DC with little resistance but has a high impedance to high frequency signals. Unlike an inductor, it's specifically designed to be lossy: the impedance is more a resistance than a reactance.
When combined with suitable decoupling capacitors downstream of the ferrite bead, this ensures that the analog section has a clean power supply with its own local decoupling: the DC current flows via the ferrite while AC transients from the digital section are blocked, and AC load transients from the analog section are supplied by the capacitor.