If you've dabbled in Christmas decorations with traditional Christmas lights, you'll know that when one bulb blows, the entire line goes out with it. Why is that? Because of how the manufacturers wire them.

That image above shows how the lights and power supply are typically wired (not the new LED varieties, though) in traditional Christmas lights. If the filaments of all the bulbs are intact, then the circuit is complete and all the lights work. But if one bulb so happens to break then the entire circuit is broken, thus making all the lights go out. It's basically much cheaper for manufacturers to build lights like this because it allows them to use this cheaper series wiring with inexpensive bulbs.

If you're interested in finding the borked bolb and possibly salvaging the lights, you'll have to perform a binary chop. Those instructions can be found here. [JGC.org via MAKE]