Flippy disk was a nickname given to single-sided floppy disks that had a second write-enabled notch cut into the sleeve so that the second side could be written to by a single-sided disk drive. Generally, these were 5.25-inch minifloppy disks, but 8-inch floppy disks could be modified in the same way, and this was possible because most of the openings on the sleeve of the disk were duplicated on both sides. It was a way of doubling the capacity of a floppy disk at a time when disks were expensive, although of course they had to be removed from the drive and turned over to access the extra capacity.
When the 5.25-inch floppy disk was introduced in 1976, all drives were single-sided. Double-sided drives were introduced in 1978, but suffered from early reliability problems. It wasn't until 1982 that double-sided drives were supported by IBM PC-DOS in version 1.1. Drives such as Apple's Disk II and the Commodore 1541 remained single-sided.
The second write-enabled notch could be made by hand, or special 'disk doubler' rectangular hold puncher could be bought to do the job. Flippy disks were also sold ready-made, and software was distributed on flippy disks that might have different programs on each side, or the same program but for different operating systems. Flippy disks sold for use in double-sided drives needed to have two index holes on either side of the hub hole.