In E-3: A Train to Catch, reaching this room is the entire aim of the mission. It has a couple of ghosts Luigi will need to defeat to light up the area, and then looking into the display itself will end the mission.
In E-4: Ambush Maneuver, the battle with the Big Boo takes place in the display located in this room. Because Luigi has been miniaturised and teleported into the display via the Pixelator, there is no way to exit the display/boss arena or explore the rest of this exhibit in this mission.
After these two missions, the Train Exhibit is irrelevant for the rest of the game.