A seemingly innocent string of Christmas lights actually has many tricks up its sleeve, most of which won't be discovered by the household tree decorator until it's too late. Christmas tree lights seem to multiply in the box, and they appear to spend most of their days braiding themselves together in Gordian knots. The final act of cruelty is the "all or nothing" lighting trick. Depending on the design, an entire string can indeed fail if only a single bulb burns out or comes out of its socket. The reason for this has to do with the nature of electrical circuits and the Christmas bulbs that depend on them.
There are two basic electrical wiring scheme used to form a string of Christmas lights. One scheme, called a series, uses a single wire connection between bulbs to light them all. The electricity from the household outlet flows down that single wire and through the first Christmas tree bulb. That bulb glows as a certain amount of electrons escape into it. The rest of the electricity continues to flow through the wire to the next bulb in the series and so on until the string is either connected to another string or the electricity flows back into the negative side of the outlet.
This series arrangement works well until one of the bulbs burns out or is removed from the socket. At that point, the electrical circuit cannot be completed, and all of the remaining lights will not glow. The only way to restore the circuit in a series lighting scheme is to replace the bad bulb with one that is known to work. Finding the bad bulb or even bulbs in a string of lights is often easier said than done, however. The known good bulb becomes a tester as each bulb is replaced individually until the string lights up again. If a new bulb is placed in an empty socket in a series, the string should light again as well.
There is a second wiring scheme which should keep an entire light string from failing because of a single bulb, but it could still happen under the right circumstances. In a parallel Christmas light scheme, two wires carry the electricity through each bulb. Theoretically at least, if one bulb's filament burns out, the remaining lights should remain lit. The second wire guarantees that the circuit will not be broken entirely. The problem with a parallel system is the complete removal of a Christmas bulb from its socket. Unless the parallel string has a special shunt installed in the socket to bridge the gap, all of the lights may still go out.
Even LED strings of Christmas lights can fail if one bulb in the circuit burns out, especially if the string is wired in series, not parallel. It is always a good idea to keep spare bulbs available for last-minute emergencies and to inspect every string of Christmas lights carefully before adding it to the tree or stapling it to the roof outside. Parallel lights can be more expensive than series lights, but avoiding the tedious task of tracking down a single bad bulb may make the investment worthwhile.