All mains lighting circuits are wired in parallel. Series wiring can occur when errors are made, or when manufacturers of decorative lighting sets use cheap designs.
This is exactly the same wiring arrangement as the diagram on the overview page. Each lamp connects to L and N, and removing one lamp has no effect on the others. Any number of lamps can be added, simply by extending the L and N conductors to other lamps.
The first lamp is connected directly to L, and the last lamp directly to N. The middle lamp is connected through the other two.
Wiring in buildings is never done in this way, but it may be found on old type Christmas tree lights.
This method has two significant problems. First, the supply voltage is shared between the lamps. As more lamps are added, they will all be reduced in brightness.
Second, the failure or removal of any single lamp will break the circuit and cause all of the others to stop working. This is why the old type Christmas tree lights were so unreliable.
If this arrangement is created in a house or other property, the effect will be that two or more lamps will be very dim, and removing one lamp will cause others to go out.
As stated above, with series wiring the voltage is shared between the lamps. Christmas tree lights often use 12V lamps, with 20 of them in series. The supply voltage of 240V is divided equally between the lamps, and as 240/20 = 12V, the lamps all work properly. A 40 lamp set would have 6V lamps.
Some tree light sets have additional devices in each lamp so that if one lamp fails, the circuit is maintained. This leads to another problem - as the number of working lamps reduces, the voltage across the remaining ones increases. As the voltage rises, the failure rate increases exponentialy, until the whole lot is destroyed in a pile of flaming wreckage.
DANGER Most sets have a 'fuse' lamp which prevents this kind of dangerous failure, but this is very easily replaced with a normal lamp, particularly if a spare 'fuse' version is not available.