From Computer History Wiki
A multi-user system is generally (the term is not precisely defined) one which several users can work on at the same time. The classic form is the time-sharing operating system, but it also includes special-purpose systems which can provide specific, limited services to multiple clients.
The term might also apply to personal computers which are set up to be shared between several people, although not all at the same time. Depending on the OS in use, and the settings of access control parameters (for OS's which have them),the system might prevent one user from examining or changing another user's files.