UNIX is a multi-user operating system.
To many people, multi-user operation refers to the idea that more than one person may be running programs at any given time. Actually, it is a little more complex than that, as even on systems that apparently only have a single user, it is quite often desirable to have certain programs running as apparently different users so that concepts like permissions are allowed to protect the computer from harm.
For example, we might have a computer which is sometimes used to conduct a home business on, and sometimes we use it for personal tasks. So, although we are but a single person, we use the computer as if we were two different users.