VM is named for its ability to run software in virtual machines which are isolated from each other; each user has the illusion of using a complete computer and can use their own operating system on this "private" computer. It initially ran on the System 360 and System 370 class mainframe machines, starting with the System 360 Model 67; it is still in wide use on IBM mainframes today.
Not all VM users have to run CMS, though; initially, some preferred to run some form of OS/360 (or later MVS) in one or more virtual machines, to provide traditional batch processing services to those users who wanted that.
Other operating systems that can now be run in virtual machines under VM include DOS, MVS, VM itself, Unix, MUSIC, and, on some systems which are used as Web servers, the operating system run in the many virtual machines is Linux.
This version of Linux used is called Linux/390, and has been largely developed by IBM. Running many hundred copies of Linux simultaneously on different virtual machines has the advantage that system crashes only affect a single virtual machine and can be easily recovered from, while the overall system keeps running.
The initial version made available to customers, CP-67, provided multiple virtual System 360 machines, although they did not have support for simulated virtual memory. It was not a true full virtual machine, though, because you could not run CP-67 under CP-67.
The next version, VM/370, announced in 1972, not only provided emulated virtual memory, but also provided such an exact emulation of the underlying hardware that it could support itself. (IBM debugged new versions of VM/370 by running it under VM/370. In fact, development of all operating systems for the System 370 relied heavily on VM/370, running on System 360 Model 67 hardware.)
See also: VM/CMS for the history of the development of the entire system, including CMS