What is the purpose of having a capacitor in Parellel to the voltage source on a DC motor?

 

It is a local DC-link capacitor. You want the motor to see a voltage source and NOT a current source. By putting a capacitor there you reduce the ammount of inductace from the DC source to the motor.

Also for high current demands, the initial blat of amps come out of the capacitor, since leads to the capacitor are inductive they will restrict large changes in current demand, but the capacitor will provide the initial blap of current to the motor