The System message is a message that can be triggered by Jagex moderators in order to broadcast to every player connected a certain event, such as holiday events, someone being the first to reach a milestone, a fix in the game engine, banning a player (this one as macroing and other offenses became a serious problem got discontinued), and a wedding event, also which might have gotten discontinued. As the game got more automated on the backend and the company got less focused directly on their players, however, system messages started to become a rare event and after 2004 there are no documented system messages occurring.
There also exists a non-interface system message which was most likely placed so as to not annoy the players having to close their windows, in case many of those messages got placed, like for instance bans for bug abuse.
A variant of the system message was placed into classic for quests, though that is triggered unicast for the player doing the quest. Some quests trigger a server message requesting information to display the user, like for example the part of the gnome language and the invasion plan.