Disk, as in hard disk or disk drive, stems from the Ancient Greek word diskos meaning 'a round flat object or kind of dish' and the verb dikein meaning ‘to throw’, which is rather fitting given the Greeks’ reputation for throwing and smashing plates. The diskos and it's Latin equivalent the discus were certainly thrown as an Olympic sport.
Disks or 'discs' appearing in computing in the 1940s as magnetic phosphor-covered disks that could be used to read or store information. The floppy disk was invented by Alan Shugart at IBM in 1967. It takes its name from the thin, flexible disk inside a hard, square plastic casing. Floppy disks were so ubiqitous by the 1980s and 1990s that most software designers used it as an icon for 'save', a trend that has continued to modern day despite the disks being obselete.