They really were floppy, could substitute as a hand fan, and were very fragile. The current style are not nearly so fragile, but they still require care. New users with iMacs may not be familiar with floppies because their machines don't use them. There are certain requirements pertaining to floppies that must be met to keep them operational. Perhaps most important is that they must be kept away from magnets.
Magnets wipe out the memory from the disk.
This is a lesson I learned the hard way. When I moved earlier this summer I packed all my computer related stuff, including a couple of large boxes of floppies, in a separate box. I moved the computer in my car, but let the movers put the box with all the other boxes. I only moved about 6 miles, but in the time it took the movers to load and unload and drive to the new place, the magnets in the stereo speakers whipped out one whole box of about 25 floppies. Don't open the metal shutter which you can do by sliding it back and forth.