This connection creates many basic circuits. Each light bulb is connected to the battery separately. As soon as a sub-circuit closes, which means that all cables are connected properly the potential difference (voltage) applied to the circuit from the battery forces the free electrons to move from the point with low potential to the one with high potential in other words from the negative pole of the battery to the positive one. These moving electrons are called electricity.
As soon as the sub-circuit closes electricity passes through the light bulb. The tungsten wire (filament) inside the light bulb becomes warm. As the temperature increases the wire becomes yellow or white and start illuminating.
The energy thus is transformed from electrical to thermal (heat) and then from heat to electromagnetic radiation (heat and light).
If for any reason one of the sub-circuit has not been connected properly this will not influence the operation of the others. Remove one of the cables. You will see that only the light bulb that is connected to it will be turn off.
The lights in our houses operate in a similar way.
Caution: if you need to change a lamp at home, you should first turn off the general power switch else you are at high risk of electrocution.
Unscrew one of the light bulbs. Observe what will happen.