Series and parallel refers to the placement of the loads in an electrical circuit.
For the purpose of this discussion, I will refer to the loads as resisters. In practice, however, the loads could be motors, lights, or a variety of other electrical devises or components.
In series, the resisters are on the same line or piggy backed from the voltage source. The circuit would leave one side of the voltage supply (-) and the current would pass through resister 1, then resister 2 and so forth untill it returned to the voltage supply (+).
Each time the voltage passes through a resister in series, there is a voltage drop across that resister. The total voltage drops across all of the reisters in series will always equal the total voltage from the source.
It is important to remember, in a series circuit, the current is the same throughout the circuit, but the voltage varies across each resister.
In a parallel circuit, one leg of each resister is on the same line (-) and the other leg is on the return line (+). They are all in parallel with the voltage source. The current across each resister is dependent on the resistance while the voltage source remains the same across each resister. As you can see, unlike a series circuit, in a parallel circuit, the voltage remains the same (always equal to the source) while the current across each resister varies .
The total resistance in a series circuit and a parallel circuit are easily found by the equations:
Series - the total R is Rt=R1+R2+R3...........
Parallel - the total R is Rt/1=R1/1+R2/1+R3/1...
The total resistance in a series circuit is always greater than the highest resister.
The total resistance in a parallel circuit is always less the the lowest resister.
Experiments can be easily set up using a simple battery, three small light bulbs and a multi meter. Simple volt and amp readings on the circuits will confirm the above discussion.
Conclusion:
Think of a string of decorative lights.
The advantage to a series light string is that only one wire or conductor is needed to go from one light to the next and so on, and then simply tie the last light on the circuit to the return - cheaper to produce, less wiring.
In a parallel light string, each light has to have both sides of the circuit on each side of the light - more expensive to produce, more wiring.
Disadvantage:
Much like the infamouse "series" string of Christmas tree lights, when one resister (light) burns out or opens, the complete circuit is open and all the current stops and, obviously, all of the lights go out.
In a parallel circuit, the voltage simply passes through the remaining lights and the only light that goes out is the burned out or open one.
In this example, a parallel circuit is much more desirable.
However, in other circuits (like when a voltage divider or different voltages are required), a series circuit would be the way to go.