A form of Mass Storage, one of the earliest popular forms and utterly ubiquitous today. It consists of a spinning disk that is read and written by a magnet called a "head." Magnetic disks are much cheaper and slower than RAM (including Flash Memory), pricier and faster than Optical Discs, and can store enormous amounts of data (in recent years reaching measurements in terabytes for larger drives compared to the gigabytes used for even the largest of other storage formats).
Disk storage devices, or disk drives, are either removable or fixed. Floppy disk drives and less popular variants such as Zip or Jaz drives are of the former type, where the disk(s) can be separated from the drive. Hard disk drives (HDDs) are of the latter type, where the disks are sealed inside the drive. Oddly enough, the HDD was actually invented first, at an IBM facility in San Jose, California in 1956; floppies weren't introduced until 1971, 15 years later, and didn't really become popular until Shugart Associates (now long since absorbed into Panasonic by way of Xerox) introduced the 5-1/4 inch "minifloppy" (compared to the original 8-inch ones invented at DEC) in 1976. For years, starting with the introduction of the Apple Disk II in 1978 and the IBM Personal Computer's 360-kilobyte standard in 1983, the floppy was one of the preferred forms of software distribution (alongside cassette tape, which hung on through the 1980s outside the US due to its lower cost), only starting to fade away once the CD-ROM hit critical mass around 1995.
The fixed HDD has become utterly ubiquitous, however. In 1980, when a floppy drive add-on kit still cost hundreds of US dollars, a PC with a hard drive was almost unheard of; by 1990, they'd become a must-have, and only the most basic PCs didn't have one. As capacities increased and the IDE interface improved, the "fixed disk" spread to game consoles starting with the Xbox and many other devices such as cameras. Flash Memory has been steadily edging in on the HDD's turf, especially in portable and high-performance desktop applications, but until the mid-2000s it was uncommon to see a solid-state drive in any PC, much less a desktop.