There's a ribbon with a small strap across it (like the keeper on a belt) on one side, and there's a cloth loop on the other. The ribbon goes through the loop, folds back, goes under the strap, and is tightened, then possibly tied in some sort of knot to keep it in place.
I Googled mostly permutations on "types of cloth fasteners", "clothing fasteners" and "old-fashioned clothing fasteners", and "types of textile closures". Went through Wikipedia's "fasteners" and "textile closures" categories.
I can draw a diagram if needed.