In order to allow the trailer brakes to be applied more quickly, what is connected to the service air line?

The service line (also called the "control line" or "signal line") carries air controlled by the foot brake or the trailer hand brake. Depending on how hard you press the foot brake or hand valve, the pressure in the service line will similarly change. The service line is connected to relay valves. These valves allow the trailer brakes to be applied more quickly than would otherwise be possible.