First released in 1974, MVS was later renamed by IBM, first to MVS/XA (eXtended Architecture), next to MVS/ESA (Enterprise Systems Architecture), then to OS/390 when UNIX services were added, and finally to z/OS when 64-bit support was added on the zSeries models; but it remains fundamentally the same operating system. Programs designed and built for MVS can still run on z/OS without modification.
MVS descends from SVS (Single Virtual Storage), which in turn descends from MVT, one of the original variants of OS/360. As the first variant of OS/360, PCP (Primary Control Program), it did not support multitasking; MVT (Multitasking with a Variable number of Tasks) was an enhancement that provided that functionality. SVS added virtual storage (more commonly known outside IBM as virtual memory), with the same address space being shared by all tasks. Finally, MVS allowed different tasks to have different address spaces.
MVS originally supported 24-bit addressing; as the underlying hardware was extended it was also to progressively support 31-bit (XA and ESA) and now (as z/OS) 64-bit addressing.
The main interfaces to MVS are JCL (Job Control Language), the batch processing interface, and TSO (Time Sharing Option), the interactivetime-sharing interface, which originally was optional but is now a standard component. ISPF is an interface which allows to accomplish the same tasks as TSO but in a menu and form oriented manner.
The system is typically used in business and banking, and applications are often written in COBOL. COBOL programs were traditionally used with transaction processing systems like IMS and CICS. For a program running in CICS special EXEC CICS statements are inserted in the COBOL source code. A preprocessor (translator) replaces those EXEC CICS statements with the appropriate COBOL code to call CICS (compare with SQL used to call DB2) before the program is compiled.
MVS systems are traditionally accessed by 3270 terminals, or by PCs running 3270 emulators; many mainframe applications these days have custom web or Windows interfaces. The z/OS operating system has built-in support for TCP/IP. System management, done in the past with a 3270 terminal, is now done through the Hardware Management Console (HMC). Operator consoles are provided through 2074 emulators. So you are unlikely to see any S/390 or zSeries processor with a real 3270 connected to it.
Files are called "data sets" in MVS; these files are organized in "catalogs". Many MVS programs expect their data files in EBCDIC rather than in the now more common ASCII. The latest versions of z/OS include support for Unicode.