What is "Power Supply Pumping"?
In general terms "power supply pumping" is the return of energy from a load to a power supply via output switches so that the power supply is forced to accept energy via an unintended path. This may lead to eg voltage rises that cannot be controlled by voltage regulators as the energy input occurs after the regulator stage. 

In the context that you are asking, if you read the paragraph headed "Supply pumping" in the datasheet referred to in your accepted answer to your prior question -
Multiple audio inputs driven by one MP3 player output - it tells you exactly what you want to know. It says


One issue encountered in single-ended (SE) class-D amplifier designs is supply 
pumping. 


Power-supply pumping is a rise in the local supply voltage due to energy being driven back to the supply by operation of the class-D amplifier. 

This phenomenon is most evident at low audio frequencies and when both channels are operating at the same frequency and phase. At low levels, power-supply pumping results in distortion in the audio output due to fluctuations in supply voltage. At higher levels, pumping can cause the overvoltage protection to operate, which temporarily shuts down the audio output.
Several things can be done to relieve power-supply pumping. The lowest impact is to operate the two inputs out of phase 180° and reverse the speaker connections. Because most audio is highly correlated, this causes the supply pumping to be out of phase and not as severe. If this is not enough, the amount of bulk capacitance on the supply must be increased. Also, improvement is realized by hooking other supplies to this node, thereby, sinking some of the excess current. Power-supply pumping should be tested by operating the amplifier at low frequencies and high output levels