The Free On-line Dictionary of Computing (30 December 2018):
A term describing an operating system or
application program that can be used by several people
concurrently; opposite of single-user. Unix is an example
of a multi-user operating system, whereas most (but not all)
versions of Microsoft Windows are intended to support only
one user at a time.
A multi-user system, by definition, supports concurrent
processing of multiple tasks (once known as "time-sharing")
or true parallel processing if it has multiple CPUs.
While batch processing systems often ran jobs for serveral
users concurrently, the term "multi-user" typically implies
Before Ethernet networks were commonplace, multi-user
systems were accessed from a terminal (e.g. a vt100)
connected via a serial line (typically RS-232). This
arrangement was eventually superseded by networked personal
computers, perhaps sharing files on a file server. With
the wide-spread availability of Internet connections, the idea
of sharing centralised resources is becoming trendy again with
cloud computing and managed applications, though this time
it is the overhead of administering the system that is being
shared rather than the cost of the hardware.
In gaming, both on PCs and games consoles, the equivalent
term is multi-player, though the first multi-player games
(e.g. ADVENT) were on multi-user computers.