Since it looks like there is another one on the other side of the coil (in picture 1), I assume it is used to create a magnetic field with that second coil. The whole second coil thing is a mystery to me? I can only think it creates the polarity that drives the motor in either forward or reverse.
But to be honest, I really don't know and am just guessing.
I am taking a guess. It may be a filter or a capacitor that acts as a filter in series with the coil and the brush. I will run the motor without this and see if sparks appear lol