A client is a system that accesses a (remote) service on another computer by some kind of network. The term originated from devices that were not capable of running their own stand-alone programs, but could interact with remote computers via some network. These dumb terminals were clients of the time-sharing mainframe computer. The client/server model is still used today on the Internet, where a user may connect to a service operating on a remote system.
See also, server.
In ancient Rome, a client was someone, usually a freed slave, who was attached to a rich patron benefactor; this was necessary for many who were not legally able to secure citizenship, a right initially reserved for the patrician class.