With this experiment you can verify that removing one of the lamps of the circuit, the other lamp fades instantly. This happens because the lamps in the circuit are disposed in serie. In an electric circuit, the electrons move from the positive pole (+) to the negative pole (-). When removing one of the lamps out of the support, the electrons flow in the string is stopped. That can be compared to traffic in a freeway. Imagine that a certain freeway, that connects city A and B, is closed and that this connection road is the only one available. It would cause no possible connection between the two cities because the cars were not allowed to circulate. The same way, in the present experiment, the electrons in the serie circuit only have a way to flow. If it is closed, the electric current becomes zero. In other words, the lamps fade because there are no electrons flowing in the circuit.
In the serie circuits several rules exist for qualitative and quantitative analysis. The current intensity in this circuit type is the same for the two lamps (resistances). On the other hand, the total resistance is equal to the sum of the resistance of each lamp. The potential is equal to the sum of the potential applied in each lamp (resistance). The electric system in your house has resistances that are associated in serie and parallel.