In the '60s when I bought my (first) Rolleiflex, these nifty small mounts were known as "the Rollei tripod mating device" or some such funny name, which always amused me. I had notions of buying two and putting them together in a dark box, hoping for "babies" which I could sell at a tidy profit - like all goodies from F&H they weren't cheap to buy even back then.
More seriously, this gadget eliminates one of the risks of putting a Rollei TLR on a tripod. The tripod screw hole (again, I'm not trying to make bad jokes here) or whatever they call the mount in-built on the bottom of the camera, is a weak point of this system. This means mounting a Rollei on a tripod could cause the bolt to shear off the tripod mount plate, the camera falls to the ground and can be damaged. It did happen to a photographer friend, a very long time ago, and cost him a fair sum to get the camera fixed - he had to replace the entire back.
I own several Rolleifixes and I use them on camera grips.
Unusually for me, I am somewhat at a loss for correct wording tonight, and anyway others have explained how the Rolleifix works, far better than I can just now. Time for a glass of wine and then to bed, I think...