What is this?

I found this wierd circuit in the base of a nikko’s DC motor and there are 3 wires coming from it. Number 1 and 2 make the motor spin when connected to a battery. But it also spins if I connect the battery to the normal place (those little metal things). And there’s also the black wire (number 3) which comes from the metal of the motor.
I can’t really understand the purpose of this circuit as the black wire seems useless and the motor seems to spin the same speed with a battery connected through it or not.
Can someone please explain me what this is?

It looks like a choke to reduce electromagnetic interference. The motor will spin a the same speed if the choke is bypassed but will generate more electrical noise. Grounding the black wire attached to the case will further reduce interference.

So where should I connect the black wire in an H-bridge circuit controlled by the arduino?

If my guess is correct, to the ground on the H Bridge.

But isn’t the ground the same as the negative in the arduino? Am I not connecting two wires to the same thing?

Yes, ground the same as the negative in the arduino, and is also connected to the ground on the H-Bridge. But this ground is not connected to the motor windings going to the H-Bridge motor output.