It's a bare or tinned copper wire laid in continuous contact with the foil screen, running the full length of the cable. Foil is thin and awkward to clamp under a terminal, so the drain wire gives you something you can actually terminate. Whatever the screen intercepts travels down the drain wire to earth.
It's tinned to slow galvanic corrosion between the copper and the aluminium in the foil, which would otherwise raise the contact resistance over time and quietly degrade the screen.
Two rules decide whether it works. Earth the drain wire at one end only, because earthing both ends creates a loop that carries current between two earth points and injects noise rather than removing it. And keep the untwisted, unscreened tail at the termination as short as you can. A screen that stops 200 mm short of the terminal has a 200 mm aerial on the end of it.