A hard disk can be divided into several partitions. Each partition functions as if it were a separate hard disk. The idea is that if you have one hard disk, and want to have, say, two operating systems on it, you can divide the disk into two partitions. Each operating system uses its partition as it wishes and doesn't touch the other one's. This way the two operating systems can co-exist peacefully on the same hard disk. Without partitions one would have to buy a hard disk for each operating system.
Floppies are not partitioned. There is no technical reason against this, but since they're so small, partitions would be useful only very rarely.