Floppy Disks were the main way to store and transfer files on computers before the advent of such mediums as CD-Rs and USB Drives.
It's not just the save icon, it's what you used to save files on before the USB drive: it's the floppy disk.
In their original form, they truly were floppy and eight inches in diameter.
They first went on sale in 19-71, by the mid 70s, a smaller format was made, coming in at just over 5 inches.
These were common for many years, and used in early home PCs such as the Apple II and the Tandy 1000.
By 1982, the format was improved even more, by making the floppy disc more durable and even smaller.
These were common throughout the 80s and into 90s. Pretty much every home computer had a 3.5” inch floppy disc drive.
But, by the late 1990s, many computers came with rewritable CD drives.
Larger disc drives like Zip drives were also becoming common. Finally, when USB flash drives become affordable, the format quickly faded.
Most modern computers don't have floppy drives built in, but inexpensive external floppy drives like this one are still available.