A series circuit is a circuit where there is only one path from the source through all of the loads and back to the source. This means that all of the currents in the circuit must flow through all of the loads.
One example of a series circuit is a string of old Christmas lights. There is only one path for the current to flow. Opening or breaking a series circuit such as this at any point in its path causes the entire circuit to "open" or stop operating. That's because the basic requirement for the circuit to operate a continuous, closed-loop path is no longer met. This is the main disadvantage of a series circuit. If anyone of the light bulbs or loads burns out or is removed, the entire circuit stops operating.
A parallel circuit has more than one resistor (anything that uses electricity to do work) and gets its name from having multiple (parallel) paths to move along. Charges can move through any of several paths. If one of the items in the circuit is broken, then no charge will move through that path, but other paths will continue to have charges flow through them. Parallel circuits are found in most household electrical wiring. This is done so that lights don't stop working just because you turned your TV off.