The knob in the lower corner of the photo turns the shaft inside the sleeve (2nd knob) with the 1/4" drive at the end of the flexible tip.
I don't know if it had a specific purpose. Will see who else weights in.
It has Blue Point USA on the end.
With the appropriate socket attached it could be used to adjust mixture screws on a carburetor or even points on a 1956 and up GM distributor(the one with the little metal door in the side).It could even be used to loosen or tighten hard to get at hose clamps.