Disk operating system
Disk Operating System (specifically) and disk operating system (generically), most often abbreviated as DOS, refer to operating system software used in most computer systems necessary to manage storage devices and the information on them (e.g., most generally data of any kind, but more commonly files of all sorts) and is called a disk operating system when the storage devices are made of rotating platters. Some DOS'es have also been named "Disk Operating System".
History
In the early days of computers, there were no disk drives; delay lines, punched cards, paper tape, magnetic tape, magnetic drums, were used instead. And in the early days of microcomputers, paper tape or audio cassette tape (see Kansas City standard) or nothing were used instead. In the latter case, program and data entry was done at front panel switches directly into memory or through a computer terminal / keyboard, sometimes controlled by a ROM BASIC interpreter; when power was turned off after running the program, the information so entered vanished.
Both hard disk drives and floppy disk drives require software to manage rapid access to block storage of sequential and other data. When microcomputers rarely had expensive disk drives of any kind, the necessity to have software to manage such devices (ie, the 'disk's) carried much status. To have one or the other was a mark of distinction and prestige, and so was having the Disk sort of an Operating System. As prices for both disk hardware and operating system software decreased, there were many such microcomputer systems.
Mature versions of the Commodore, SWTPC, Atari and Apple home computer systems all featured a disk operating system (actually called 'DOS' in the case of the Commodore 64, Atari 800, and Apple II machines), as did (at the other end of the hardware spectrum, and much earlier) IBM's System/360, 370 and (later) 390 series of mainframes (e.g., DOS/VSE: Disk Operating System / Virtual Storage Extended). Most home computer DOS'es were stored on a floppy disk always to be booted at start-up, with the notable exception of Commodore, whose DOS resided on ROM chips in the disk drives themselves, available at power-on.
In large machines there were other disk operating systems (eg, IBM's VM, DEC's RSTS / RT-11 / VMS / TOPS-10 / TWENEX, MIT's ITS / CTSS, Control Data's assorted NOS variants, Harris's Vulcan, Bell Labs' Unix, and so on. In microcomputers, SWTPC's 6800 and 6809 machines used TSC's FLEX disk operating system, Radio Shack's TRS-80 machines used TRS-DOS, their Color Computer used OS-9, and most of the Intel 8080 based machines from IMSAI, MITS (makers of the legendary Altair 8800), Cromemco, North Star, etc used the CP/M-80 disk operating system. See list of operating systems.
PC-DOS/MS-DOS (and CP/M)
The best known family of operating systems named "DOS" is that running on IBM PCs type hardware using the Intel CPUs or their compatible cousins from other makers. The original was licensed to IBM by Microsoft, and marketed by them as "PC-DOS". It was first developed at Seattle Computer Products by Tim Patterson as a variant of CP/M-80 from Digital Research, but intended as an internal product for testing SCP's new 8086 CPU card for the S-100 bus. It did not run on the 8080 (or compatible) CPU needed for CP/M-80. It was called QDOS, among several other names. Microsoft licensed it from SCP, made changes and licensed the result to IBM (sold as PC-DOS) for its new 'PC' using the 8088 CPU (internally the same as the 8086), and to many other hardware manufacturers. In the later case it was sold as MS-DOS.
Digital Research produced a compatible variant known as "DR-DOS", which was eventually taken over (after a buyout of Digital Research) by Novell. This became "OpenDOS" for a while after the relevant division of Novell was sold to Caldera International, now called SCO. There is also a free version named "FreeDOS".
See also: List of DOS commands