DOS (Disk Operating System) is a generic name for a variety of 16-bit text-mode operating systems. (Note that "DOS" is pronounced dahss or doss but not dose.) The archetypal example is MS-DOS, Microsoft's long-running OS that was also sold by IBM as PC-DOS. MS-DOS (and PC-DOS) originated as 86-DOS (eventually renamed QDOS) from Seattle Computer Products, which was intended to be a CP/M clone. Other (modern) examples include DR-DOS and FreeDOS.
DOS by itself had no graphical interface; instead, if one was desired, users had to buy one seperately. Several GUIs were available for DOS, but Windows displaced them all with version 3. DOS was still present in Windows 95, 98, and Me, but is totally absent from all NT-based versions (including NT, 2000, XP, Vista, and Windows 7), instead being emulated (via NTVDM and cmd.exe).
Early versions of MS-DOS and PC-DOS included a BASIC interpreter (basic.exe), followed by BASICA, GW-BASIC, and finally QBasic. (QBasic wasn't installed by default under Windows 9x; it had to be copied from the install media.) There are compilers and/or interpreters for pretty much every programming language available for DOS.
Before the rise of MS-DOS, the term DOS was used for a specific case of OS, one that was able to use a disk drive (as opposed to things like tapes and punch cards), thus "disk operating system". There have been a number of operating systems called "DOS", besides the ones discussed here, many of which are completely different systems. (For a fairly complete list, see Wikipedia's list of disk operating systems.)