Usefulness of measuring 0v using ADC
That quote you mention says it all really.  It's purpose is to discharge the Sample And Hold capacitor.

That capacitor is used (as I'm sure you are aware) to store the incoming voltage while it's being sampled by the ADC.  The ADC operated in two main phases:


Acquisition
Sampling


During acquisition the capacitor is connected to the incoming voltage.  During sampling it is disconnected from the incoming voltage and the voltage it stores is read into the internal registers.

It takes a certain amount of time for the voltage in the capacitor to equal that of the incoming voltage.    If you try reading at higher speeds then what voltage was in the capacitor from the previous sample can affect the new reading.  However, if you do each sample always from a known voltage in the capacitor (0V) then you get much more stable results.

Another good use for it is when using the ADC as a Charge Time Measurement Unit.  This is the proper way of performing capacitative sensing.  You apply a constant (tiny) current to an external capacitor (the sensing plates) for a specific period of time.  When that time is up you disconnect the constant current source and measure the voltage that has developed across that capacitance.  The capacitances and currents are small, and if there is a charge in your S&amp;H capacitor at the time you do the sampling that will be back-fed into the touch sensor capacitative plates changing the voltage.  By ensuring that the S&amp;H capacitor is at 0V before you sample the plates you won't be adversely affecting the voltage on the plates with successive readings (well, you will, but it will be consistently in the same way every time so it won't affect your overall results).