The disk notcher is a type of hole punch with a rectangular hole and a perfectly sized and shaped body to quickly and easily punch a hole in exactly the right place in a 5¼" floppy disk and result in a flippy disk.
Of course, there are other ways to cut a small notch in the side of your disk. Many people use a single-hole punch and cut a semi-circular hole. This usually works ok, but occasionally, several holes must be punched before exactly the right spot is hit. The disadvantage here is that your disks now take on a 'mangled' aesthetic instead of the professional, precise and symmetrical look of a properly notched disk.
A craft knife could, of course, be used, but would be rather inconvenient. Careful measurement and cutting; needing a cutting board and straight edge - all of which could be done away with by the disk notcher's instant operation.
There is one caveat to using the reverse of a disk in a single-sided drive which is often overlooked. Even when reading a disk using a double-sided drive, the disk spins in a single direction. The inside of the case is designed to catch dust and protect the disk and drive heads. By flipping the disk, you change the direction in which the disk spins in its case and potentially dislodge dust particles causing errors or more lasting damage.
This is mostly a theoretical problem, and most people use notched disks for many years without problems.
Although single-sided drives exist - historically, at least - 3½" floppy disks can't be flipped because the hub is only available on one side of the package - the other side being a solid base for affixing a large label. However, as mkb points out, notchers exist for these disks because there's a hole on one corner to differentiate high-density (1.44MB) disks from double-density (typically 720-880KB). Again, use of a simple tool to get more from a disk than it was originally intended to offer.