Originally QDOS, for Quick-and-Dirty Operating System, it was purchased by Microsoft from some now-entirely-forgotten company for a paltry $25,000. Microsoft subsequently sold it to IBM on a royalty-per-copy-sold basis, for use in their original IBM PCs. This brought Microsoft to a position of incredible power, as other companies began making PC clones, and Microsoft sold the OS to them, too.
DOS is hardly an OperatingSystem at all. Mostly, it's a FileSystem, with calls for accessing files from both floppy and hard disks. There is also a shell (good ol' command.com) which loads programs into memory and runs them. Other than that, DOS programs were basically on their own, free (and required) to mess with the PC's hardware at will.
DOS has generally fallen out of use; occasionally it will be used in EmbeddedSystems because it's small and doesn't get in the way of hardware.
If you've ever wanted to play your old DOS games, but your PC was too fast, or WindowsOs didn't play well with it, you may be interested in the DOSBox emulator, which emulates an x86 and the DOS filesystem calls.