They play analogous role to cable releases on most bikes, e.g., those with V-brakes. They allow you to temporarily shorten the cable housing so that you can spread the brake pads farther apart and pull out or push in the wheel without deflating tires.
In the case of the BYB the cable adjustment gizmo is not used when a wheel is removed but between the folded and unfolded states.
Is there something about the BYB's fold that affects a brake cable to where the brake drags on a wheel in the folded state?