In a multicore cable, what is the nylon "string"?

If the thread is just inside the outer jacket (also called a sheath), it is likely a ripcord. It's meant to be used to strip the outer jacket without harming what is directly under that jacket (shield, bundle of conductors, etc.).

This video demonstrates how to use a ripcord.

That string can be used to strip the jacket off of the cable.

You nick the cable at the end, put the string in the cut, then you can pull the string back and it will cut through the insulation on the way back.

For tough insulation (or soft fingers!) you might want to to tie a loop in the end first.

Marker threads (see Andy aka’s excellent answer) tend to be weak.

If it’s a strong nylon thread that’s outside the shield it could be a “ripping cord”. They can be pulled back to slice through the outer insulation. They’re more common in larger cables than the image, but you also see them in UTP: