I am not sure what is supposed to be shown on this screen on only one tram that I know of, but I would guess it is for advertising. It doesn't appear to work and has been scratched and marked already. I could either suggest Sydney is very civilised or not very civilised because I recall buses having scrolling advertising in the 1980s.
Maybe the screen is to give passengers a visual of the people from the tram control centre who are so frequently heard to say, more often than not with a thick accent, Yarra Trams apologises for any inconvenience caused. It would be interesting to put a face to a voice.
A similar picture to the one below of Yarra Trams control centre was often featured in promotional advertising a couple of years ago. This one is from vicsig.net It shows how modern the system is and how they have cameras out on the street monitoring the tram system. It makes it seem very odd that while they have a camera at the corner of Flinders and Swanston Streets, a very busy intersection, that they do nothing about cars in Flinders Street blocking the intersection and delaying trams. Do they just watch the trams on the screen or do anything about problems they see?