An old-fashioned 5.25-inch floppydisk, commonly used in early personal computers (such as Apple IIs and IBMPCs). So nicknamed because, unlike 3.5-inch floppies, they are flexible enough to bend when waved (that is, they flop around).
I should put a 5.25" drive in my old computer and see if there are any DOS games I want from the old floppy floppies.
Person A: "Can I borrow a floppy disk?"
Person B: "Hard floppy or floppy floppy?"