Looks like the physical storage medium of a 3 1/2 inch diskette. Which is usually called a 3 1/2 inch floppy disk, except with this one it's a bit of a misnomer, since this iteration has a rigid case, unlike the older 8 inch and 5 1/4 inch versions. Or should have, it appears to be removed in OP's case.
The disk itself is flexible, hence the floppy disk. In contrast a hard disk had rigid platters, hence hard. The outer casing has nothing to do with it.