Also called a loop turner or bodkin.
This tool is primarily designed for making rouleaux when sewing (small, narrow, turned-out fabric tubes for e.g. straps, button loops, etc.).
It is also very practical for threading cords, elastic, and other items that come out of hoodies, waistbands, etc. in the washing machine. It can also be used to replace worn cords, etc. A practical tool that makes fiddly repair jobs simple :)
You thread the entire rod through the casing and then push the tip of the hook through the end of the elastic/cord/ribbon, and then simply pull the rod back out, bringing the cord with it, which is locked in place by the small flap.