HopiQ wins the "prize" for the most detailed answer! *Smiles!*
It is indeed a ruffler, and since she explained it so well, I'll let her do it here:
I have one of these exactly like yours! And I even used it recently. My grandma (who is no longer living) gave me all her sewing machine attachments several years ago. It may even have been when I was in high school. (Time flies!) Many I don't use, but this one does come out from time to time. It is so handy! It is indeed a "Ruffler." It attaches where an ordinary sewing machine foot would attach, but it also needs to engage with the little doo-hickey that tightens your needle into place. The little numbers indicate how often the ruffler will make a tuck (every stitch, every six stitches and so on). You can play with your stitch length as well to change how your ruffle comes out. I use it when I need to make a long ruffle from a strip of fabric to use as trim. It creates evenly spaced tucks and very pretty trim. I've used it on flat lace and strips of hemmed fabric. I have the instruction paper that came with mine. Let me know if this was just for fun or if you actually need to know how to use it!
When I was putting away my Christmas tree, I took a picture of my tree skirt. I made it several years ago, and used the ruffler attachment. It worked marvelously! It not only gathers or tucks the fabric (or in this case, I used organdy ribbon), but it will attach it to a flat piece of fabric as you're stitching!
Here's the tree skirt:
It is a pretty amazing attachment!