Dear Student
A series circuit has only one path for the current to flow through all the devices in a row and back to the starting point. The same current flows through each part of a series circuit. If the circuit is broken at any point there won’t be any current that will flow. So if one of the bulbs blew out, the other bulb would not be able to light up because the flow of electric current would have been interrupt.
In parallel circuit there more than one path for the current to flow. In this case, because electricity can flow in more than one path, even if one of the bulb blows out, the other bulb will still have electrons flowing through it and it will continue to glow.
Regards