Alas, on sailboats, pretty much every line is called a jackline.@Joe is correct. It is called a jackline and lets the lower part of the sail fall away so it doesn't bunch up at the reef point.
Mark
I had one, a jackline, on my Mark 25 which was a super up C&C 25. I never understood why it was rigged like that. The boat went out of my life thirty years ago so I have no recollection or way to quantify if reefing was easier or not.The thin line connects the sail's luff to the slides. It allows that lower section of sail to pull away from the mast while the sliders stay in place when the mainsail is lowered for reefing. Instead of a bunched up sail, there is easy access for the first reef point to clip into the rams horn, while the "slab" can be pulled away and then rolled up and tucked in snugly on the boom. When hoisting, sliders are already inserted in the slot, the guiding lines pull the sail into alignment with the mast. There's a term for it that I can't remember.
Many sails now come equipped with a strap and ring device for getting the reef point over the bunched sail to the rams horn.
The system was employed to speed up reefing. I think it is pretty effective in that regard.