Signals and schedules make it possible to add an extra without causing a bottleneck or an accident. Those cars go to a transfer point, where they are handed over to the westbound railroad. In this case, it is the Nickel Plate Road. The cars are taken from the Lackawanna and assigned to a westbound Nickel Plate train. The same process is used between Buffalo and Chicago.
Passenger trains work much the same.
A train known as an express or limited, because it only makes a few stops, would be scheduled to run regularly between Hoboken and Buffalo. It would only stop, perhaps, at Scranton, Binghamton, Ithica Junction and Buffalo. That would be fine for anyone going to one of those destinations. For instance, a passenger wishes to go to a point between Scranton and Binghamton. He would take the express to whichever city was closest to his destination, then debark and transfer to a local.