The hook (with the decorative waves) allows the sheath to be hung in the armpit opening of one's waistcoat, or in the coat sleeve.
I'm having a hard time picturing how that would work. Since the handle of the knife sticks out several inches past the end of the sheath (where the clip is), how could it hang from the arm hole of a waistcoat? I'd think the handle would be too long and be sticking up into your armpit, preventing you from being able to put your arm down.