A series circuit has more than one resistor (anything that uses electricity to do work) and gets its name from only having one path for the charges to move along. Charges must move in "series" first going to one resistor then the next. If one of the items in the circuit is broken then no charge will move through the circuit because there is only one path. There is no alternative route. Old style electric holiday lights were often wired in series. If one bulb burned out, the whole string of lights went off.
An example of a shematic diagram of a series circuit:
