I have used this technique before (on 4 layer, not 2, but it still holds), and I found several advantages and drawbacks of doing this. What they are specifically talking about is an island of ground plane that is not GND, but AGND, which is tied to GND at one single point, possibly through a small impedance. I'm not sure if the ATMEL has a separate AGND pin, but our dsPIC did. In this case there is no connection but an inductor between VCC and AVCC, and bypassing should never cross from VCC to AGND, or AVCC to GND. All analog signals are referenced to AGND (i.e. volt-dividers, anti-aliasing caps, etc). The whole point is to keep all the noise-creating digital circuits from dirtying up your analog rails.
As far as implementing their technique, they are just saying that the extents of this AGND island would roughly encompass this corner of the micro, as well as all bypassing between AVCC and AGND and your analog measurement circuits. It doesn't have to extend all the way to input ports for voltage measurements, etc, but at least to the low-side resistor of your volt divider and antialiasing cap, as well as any analog input amplifiers and their power supplies. By AVCC, I'm referring to the VCC after being filtered by the inductor.
We experimented with different impedances that connected GND and AGND, and found a 10 ohm resistor worked well to isolate the noise on the digital ground. If the impedance is too high, the micro will not be happy because it does expect the same DC potential on the two grounds. In our case, we had a separate low-noise LDO feeding the AVDD, and a high-power, noisy buck converter feeding the many devices on the digital VDD. The isolation you would achieve (to keep the noisy digital stuff from polluting your analog rails) is less with just an inductor and a separate ground island as this datasheet suggests, but it is much simpler to implement.
A simple test to check if you are improving your analog rail noise is to use your ADC to convert a DC value, and plot the raw measurements on a histogram or do a stdev in Excel. In a perfect/noise-free world, you would have no variance in this measurement, but in the real world you have a certain amount of variance proportional to your noise levels.