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. They are so useful that, after living with them for a while, you ponder how you could lived without them before.
Can that Shimano or alternative be used on a Brompton?
It's a (small) pain to have to deflate the tires when I get a flat.