What is the difference between a step-up and a step-down ring?
I want to put a large diameter filter on a small diameter lens.
Do I need a step-up ring or a step-down one?
A step-up ring allows you to fit a filter that has threads larger than your lens. A step-down ring does the opposite (with possible vignetting issues).
If you have 72mm lens threads and want to fit a 77mm filter, you need a step-up ring. If you have 77mm lens threads and want to fit a 72mm filter, you need a step-down ring.
So in your case you want a step-up ring.