What is the diff between "Analog Power Supply" & "Digital Power Supply", and "Analog Ground Supply" & "Digital Ground Supply"?

Digital things are noisy, they usually creates voltage ripple on digital supply (and ground) bus. That's why for precision analog circuits it's good to have separate (analog) supply which will be much "cleaner" than digital supply. Low noise analog design needs not only clean supply but good PCB layout including proper ground plane design and proper decoupling of both - digital and analog supplies.

Brett Kuntz said:

I don't really understand how some power could be for digital things and other power for analog things? How can power be different?!?! I'm confused lol.

The point is that voltage may vary, even if it comes from the same power source. PCB traces have a resistance. As soon as a current flows, this means a voltage drop along the trace. So the voltage isn't the same everywhere on a PCB, even if connected to same power source. And it changes with the momentary current consumption.

Digital circuitry, especially CMOS circuitry, has the habit of causing short current peaks when their state changes, and consuming very low or no current while static. During these current peaks, there is a corresponding peak in the voltage drop over the supply traces, causing the supply voltage to drop. Not a problem for digital circuitry, but a huge problem for analog circuits, especially references, amplifiers and AD/DA converters. To smoothen this influence, you have external blocking capacitors (they are blocking the propagation of the current peaks across the whole PCB, acting as a low-pass R/C filter together with the trace resistance),. However, they won't help for the currents inside the chip.

For this reason, the bigger MSPs have a separate input for the analog supply, where there are no peaks on current consumption. The analog supply voltage may be directly routed from the power supply (separately form teh digital supply trace) or conntected to the digital supply by a low-pass filter (e.g. a 10 to 100 Ohms resistor followed by a 10µF tantalum/100nF ceramic capacitor combo between AVCC and AVSS).
Teh analog ground should be reouted separately from the MSP to the supply GND point, so the operating currents of the digital circuitry do not flow on it and do not cause ripples on the 0V reference for the anlog part.