1. <person> Someone doing "real work" with the computer, using it as a means rather than an end. Someone who pays to use a computer. A programmer who will believe anything you tell him. One who asks silly questions without thinking for two seconds or looking in the documentation. Someone who uses a program, however skillfully, without getting into the internals of the program. One who reports bugs instead of just fixing them. See also luser, real user.
Users are looked down on by hackers to some extent because they don't understand the full ramifications of the system in all its glory. The term is relative: a skilled hacker may be a user with respect to some program he himself does not hack. A LISP hacker might be one who maintains LISP or one who uses LISP (but with the skill of a hacker). A LISP user is one who uses LISP, whether skillfully or not. Thus there is some overlap between the two terms; the subtle distinctions must be resolved by context.
2. <jargon> Any person, organisation, process, device, program, protocol, or system which uses a service provided by others.
The term "client" (as in "client-server" systems) is rather more specific, usually implying two processes communicating via some protocol.