The ad's byline calls it a saddle horse substitute, and looking at the mechanism, it appears the part you sit on was sprung and could move somewhat independently of the base.
So I'm guessing, you would hold onto the handles and then move the seat back and forth a bit like a modern rocking chair perhaps? Maybe it could provide a small amount of exercise in the process. Even some upper body workout if you used primarily your arms on the handles to supply the force.
How that translates to the most important health mechanism ever produced is left as an exercise for the reader.







Allan Sherman himself wrote a spoof about Digit Dialing!
https://youtu.be/watch?v=hCFLanFgUPI