I will try to find the papers I read about this. I think they were by an engineer at TI. They were more articulate than me.
Essentially, ground does a couple of jobs:
1. ground is every signals return connection, carrying the complementary current to 'balance' the signal. PCB tracks are low resistance, but this varying curent still shows up as a varying voltage on ground. If digital and analogue ground can be separated, the analogue ground will be more stable allowing the ADC's to measure with greater precision and accuracy because it won't carry current (and hence small voltages) for rapidly changing digital signals.
One of the techniques is to partially disconnect areas of the ground plane. The remaining copper connection between the ground areas is an inductor, which connects for DC voltages and very low frequency changes, but increases in impedance, and hence filters high frequency changes from traveling through neighbouring areas of ground.
A better technique is to try to keep analogue and digital apart, and not intermingle their signals.
2. varying voltages in a track induce voltages in neighbouring tracks (think of an electrical transformer), the faster the variation, the bigger the effect. The ground plane can be used to 'isolate' and hence 'contain' those variations to a much smaller area of the PCB by acting as the neighbouring track. The ground plane under the signal track is like the other transformer coil, the return signal travels along the ground plane underneath the signal track (there is no need to shape the ground plane to achieve this, keep the ground plane continuous under the signal, and physics does the heavy lifting).
Summary: a ground plane can 'contain' or 'steer' induced voltages away from neighbouring signal tracks, and 'cuts' in the ground plane can filter higher frequency noise, preventing it from spreading across the board, and 'polluting' sensitive analogue signals with digital 'noise'.