In a series circuit all the components are joined end to end in one single loop, so there is only one path for the current. The current is the same through every component. The potential difference of the supply is shared between the components. If one component breaks, the loop is broken and everything stops, so if one lamp in a series circuit blows, the other lamp goes out. Adding more lamps in series makes each lamp dimmer, because the potential difference is shared between more lamps.
In a parallel circuit the components are on separate branches. The current from the supply splits at a junction, flows through the branches, and joins up again. The total current is the sum of the currents in the branches. Each branch has the same potential difference as the supply. If one branch breaks, the other branches still work, so if one lamp in a parallel circuit blows, the other lamp stays lit. Lamps in parallel each keep the same brightness however many are added.
