Effect of a coil before DC motor
It is an common mode choke used for for suppression of electromagnetic interference and radio frequency interference from power supply lines.

Both the supply lines will be wound around a single core.



Source: https://en.wikipedia.org/wiki/Choke_(electronics)#/media/File:Slionnnnnn1.jpg


  I think the coil was responsible for somehow making the motor more powerful.


No, it is not like that.. it will increase the power supply quality and helps the electronic components and devices operate the motor with out malfunctioning