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I am wondering what effect a coil before a DC motor has.

enter image description here

It's a 3 AA battery powered (4.5V) small RC car. I cut off the cables going to the motor and connected the motor to the battery directly (I soldered connecting cables first). I also did experiments with a Raspberry and a L293D motor controller always using the 3 AA batteries. All works fine, however, I believe that the motor was more powerful in its original state with the coil.

I unwound the coil. Each cable was spinning 8 times around the small metal hull. I think the coil was responsible for somehow making the motor more powerful. I just don't understand the logic how.

(photo shows the original state as I bought it)

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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

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