The idea behind a carbon arc light / lamp is that electricity "likes" to jump from one piece of carbon to another, creating an arc of electricity in mid-air. The tips of the carbon rods start to heat up more and more, and eventually to the point where they produce A LOT of light.
For a while, carbon arc lamps competed with your everyday light bulb, but the light bulb won out, and now probably provides most of the light in your home. A lot of people didn't like the harsh white light of the arc lamps, and sometimes the lamps would make a sound around 10,000 Hz that was really annoying. Of course, our good friend Tesla saved the day on that. :P
For a long time, nobody could match the sheer power of arc lamps, (at the time, they were about 200 times more powerful than filament bulbs), and so they were used in spotlights and movie theaters.
And now, you can have your own carbon arc lamp!
I finally found the jumper cables! The car battery-powered light is very impressive, and produced a glowing blob of light about an inch in diameter, which I assume was the electric arc. I'll have to take a few pictures through my welding goggles if I can find them.