An environment which allows you to interact with a remote computer “as if you were sitting in front of that computer”. The computers don't have to be of the same type, nor do they have to be running the same OS: they only need a working TCP/IP network connection.
This is the computer to be controlled without the need, or the possibility, to be actually sitting at its console. It is remote from your location. Also called the “server”. In our example scenario this is the computer of the user you are assisting.