Why should we couple AGND and DGND?
The 'ground' is the reference voltage for a signal.  For instance, on the left, you have an ADC block.  The ADC reads the voltage into that block with reference to AGND and saves that voltage into some registers.

Once the digital side of that block decides to interface, then the digital signals are read with reference to the DGND.

Unfortunately, unless the IC or circuit is specifically designed for isolation, the DGND and AGND of most parts cannot be significantly different or bad things will happen on the silicon.  We try to separate AGND and DGND from a layout (and often schematic) standpoint to reduce the interference between the two circuit references.  There are books written about how to do this well.