it's called a Dooley Foot, the neat think is having that slide on part. I've seen some in the back clamp and side clamp style missing the slide on attachment.
This is what they instructions say it can do:
"One foot sews eight ways: Hemstitching, Picoting, Embroidering, Crochet foundation, Binding, Tucking, Shirring, Smocking and Regular sewing"
At some point, Singer also made a multi-purpose foot called the Style-O-matic. That is the expensive one. From what I've read it's not that easy to use and using a single purpose foot for the application gives much nicer results - still something fun to have though.
Plain Stitching, French Seams, Binding, Tucking, Edge-Stitching, Fancy Edgings, Lace Insertions, Shirring, Ornamental Stitching, Invisibly Stitched Braiding, Shirring & Ornamental Stitching, Shirring and Invisibly Stitched Braiding, Smocking, Piping, Hemstitching, Picoting, Crochet Edge .