What happens to the light bulbs in a series circuit?

They all have the same level of current in each, the supply voltage is split across each one. If all the lamps or "bulbs" are of the same wattage and therefore the same resistance then the voltage across each will be the same.

WARNING:

Be careful with Christmas tree lights, they are in series!!

If one blows they all go out but you then have the full mains voltage at the point where the blown lamp - bulb is!

So unplug them first if you know which one has blown, it is much safer to test each lamp with a multimeter than try to find the blown one using a new lamp - bulb in each of the lampholders.