Yes, as mrpearson says, I'd expect this to be the braided shield wire for the cable that's been taped or heat-shrinked. I'd have expected them to have left a small section of bare end. Other pickup makers would have wrapped the bare shield wire around the signal ground wire, soldered the ends together and then put some heat shrink over the wound wires to prevent it from accidentally touching a signal connection and causing silence.

Just cut back about 1cm of the blue-circled wire's insulation and it should be obvious that it's the braided screen wire inside. If so, it just gets soldered to ground on the back of a pot. It doesn't need to be wrapped around the black wire - that's just done for neatness and convenience.

What you will need to do is put some insulating tape or heat shrink over the bare ends of the soldered together white and red wires. The pickup signal passes through these wires and you don't want the ends to accidentally get grounded otherwise you'll end up with a single coil sound, not a humbucker sound, from the pickups.