Why do we use capacitors in parallel with DC motors?
Generally a 0.01~0.1uF capacitor is wired across brushed DC motors to reduce radio frequency EMI caused by arcing between the brushes and commutator. Sometimes two capacitors are wired in series, with the center connection going to the case to 'ground' it at RF frequencies. 

For best effect the capacitor(s) should be placed on or inside the motor. In this case a capacitor has been included on the driver board. This makes it less effective at higher frequencies because the wires from the board to the motor will still be able to radiate EMI. Still it's better than nothing, and may prevent misoperation due to interference from an unsuppressed motor getting into the driver and input wiring.