A "remote user" is how a woman might refer to her husband while he is watching TV. In the computer world, however, a remote user is someone who works on a computer from a remote location. For example, if Bob leaves work and forgets to bring a file with him from his office computer, he might be able to connect to his work machine from his home computer and grab the file. When Bob accesses his office computer from home, he is considered a remote user.
Of course, Bob does not want anyone to be able to access his computer remotely. So, he would most likely need to enter a username and password in order to connect to his office machine. Programs like Timbuktu and PC Anywhere allow users to not only connect to their computers remotely, but actually display the interface of the remote machine on their local computer. Unix-based systems such as Mac OS X and Linux allow users to control the computers remotely using the text-based "Terminal" interface. Remote connections can be made over a local network, a direct phone connection, or over the Internet. Of course, the slower the connection, the slower the response time will be from the remote computer.