It is a fairly straightforward concept: One person gets the headlight and cycles in the front. The other gets the tail light and cycles at the back. You ride in as tight a procession as possible, never separate and never change positions. In this manner, you essentially become a tandem bicycle, with one complete set of lights.
I forget when exactly it was that I tried this for the first time, but I remember being impressed with how well it worked. I kept my tail light on my own bike, and gave a speedy friend my powerful headlight, which was bright enough to keep his rear wheel visible enough for me to latch onto. We cycled home as one efficient, illuminated machine, and I got to practice my paceline skills in the dark!
Apparently the night train was once a not uncommon method of sharing lighting, to save both weight and money. One friend tells me stories of him and his father sharing lights in this manner, when they toured together in the 1970s with a set of what he describes with a shudder as "utterly brick like torches." According to another, they used to form "night trains" on club rides on a regular basis, until new rules put a stop to the practice.
Needless to say, sharing lighting is not as safe as each rider having their own set of powerful lights, and would be stressful to maintain over long distances. But in a pinch it does provide a solution. After all, not all of us are prepared for all eventualities 100% of the time. The "night train" is a useful emergency option to keep in one's arsenal.