Why is it that when you put two electric lamps into a circuit in parallel with one another, the current through the circuit increases, while when you put those two lamps in series with one another, the current through the circuit decreases?
When the two lamps are in parallel with one another, they share the current passing through the rest of the circuit. Current arriving at the two lamps can pass through either lamp before continuing its trip around the circuit. The two lamps operate independently and each one draws the current that it normally does when it experiences the voltage drop provided by the rest of the circuit. With both lamps providing a path for current, the current through the rest of the circuit is the sum of the currents through the two lamps.
But when the two lamps are in series with one another, each lamp carries the entire current passing through the circuit. Current arriving at the two lamps must pass first through one lamp and then through the other lamp before continuing its trip around the circuit. There is no need to add the currents passing through the lamps because it is the same current in each lamp. Moreover, the voltage drop provided by the rest of the circuit is being shared by the two lamps so that each lamp experiences roughly half the overall voltage drop. Since lamps draw less current as the voltage drop they experience decreases, these lamps draw less current when they must share the voltage drop. Thus the current passing through the circuit is much less when the two lamps are inserted into the circuit in series than in parallel.