As Molleur says, it's a plastic tube that varies the ignition timing depending on the vacuum at the inlet manifold.
Throttle(s) closed = big vacuum and little ignition advance so it doesn't stall as it slows to an idle. Throttle(s) open = less vacuum and lots of ignition advance so the spark fully ignites the fuel/air mix before the firing stroke piston has travelled back down the bore at higher revs.
Cheap as anything and available from most motor factors so not worth trying to repair.
https://www.rimmerbros.co.uk/Item--i-37H4229M
https://www.rimmerbros.co.uk/Item--i-128262
https://www.rimmerbros.co.uk/Item--i-12B2095