Ghosting is the (tenuously attributed) name for when the admin of a server, instead of being inside the room, watches the console window of the server software, which supplies chat logs, and then speaks through it into the room. This means that the admin can check that everything is OK in the room, without having to enter it in-game.
Method
To speak into the room, the admin uses the /say command on the console window. Their message appears in the room as though an op had used the command; it is yellow text with no player name. This confuses players who don't know about the process of ghosting.
Terminology
The name comes from the fact that the admin has no physical manifestation in the room, and is a disembodied voice.