Why is it when you plug in a string of holiday lights and notice that the entire string turns off when you remove one bulb?

Because it is on one connection at least that is the old type the new ones are not connected they are ap alternating polaritys

There are two ways to make connections with electricity, series and parallel. If you were to connect two batteries in series, like in a flashlight, the voltage would be the total of the voltages of all the batteries, but the amperage would be the same as one battery. A series connection is the positive side of the first battery runs to the negatve side of the second battery and so on.

Parallel connections connect the positive terminals together and the negative terminals together. The voltage stays the same, but the amperage increases.

Still awake? Connecting things in series only requires one wire between them. Parallel connections need two. Strings of lights can be manufactured cheaper if they're in series, but if any bulb burns out, the whole string dies. Strings that are wired in parallel are more expensive to manufacture, but if a bulb dies, one bulb goes out. The rest are still on.