What is a series circuit?
A series circuit is one in which only a single path exists for current to flow through.
A wire loop extends outward from a power source before returning to complete the circuit. On that loop, one or more devices are placed in such a way that all the current must flow through each device in order. This picture shows lightbulbs on a series circuit:
This can be particularly beneficial in terms of connecting multiple cells together (we usually call them "batteries," although the term battery refers to the series of cells). By sending all the current through multiple cells, a larger gain in voltage can be achieved.
Series circuits have their drawbacks as well - if one device on the circuit fails, they will all shut off, because the current is no longer able to flow through any of them. This is what makes series circuit Christmas lights so frustrating - one bulb goes out, they all go out. Then you have to try changing one bulb at a time to try to find that one that failed. Yuck.