The hard drive is what stores all your data. It houses the hard disk, where all your files and folders are physically located. A typical hard drive is only slightly larger than your hand, yet can hold over 100 GB of data. The data is stored on a stack of disks that are mounted inside a solid encasement. These disks spin extremely fast (typically at either 5400 or 7200 RPM) so that data can be accessed immediately from anywhere on the drive. The data is stored on the hard drive magnetically, so it stays on the drive even after the power supply is turned off.
The term "hard drive" is actually short for "hard disk drive." The term "hard disk" refers to the actual disks inside the drive. However, all three of these terms are usually seen as referring to the same thing -- the place where your data is stored. Since I use the term "hard drive" most often, that is the correct one to use.