Superimposed ignitor is a type of ignitor, which essentially has a HV generator output in series with the lamp. So by that the main ballast output is connected in series with this HV generator output, so their voltages sump up, aka "superimpose". The "HV generator" is in fact the secondary winding of a step up transformer driven by a pulse from the pulse circuit. The transformer works only for narrow / high frequency pulses, for the mains frequency operating current it forms essentially a short circuit (because of its rather low inductance).
An example is
here .
The main benefits are first the main ballast with its dense winding is not exposed to the HV pulses, only the wire between the ignitor and lamp is. It is way easier to make the rather small HV transformer in the ignitor to withstand the high voltages, than the whole bulky and mainly hot main ballast assembly. So beside higher reliability (the hot ballast is not exposed to high voltage, while the ignitor operates at rather low temperatures because there is not much wire resistance passing the lamp current there) it allows for really high voltage ignition pulses (7kV were quite common for HPS in the 80's here). And the rather small ignitor does not have to be physically placed with the ballast, so could be with just the lamp, so allows large distance between the lamp and the heavy ballast, without that long cable affecting the ignitor performance, the rather small and lightweight ignitor is placed with the lamp and the cable between the ballast and ignitor is going the long distance. The disadvantage is, because the HV secondary has to be of low impedance for the main operating current, its inductance is limited, so it can generate only rather narrow ignition pulses. That means the distance between the ignitor and lamp is really limited then. This could be countered by operating the ighnitor at HF AC bursts, but that then makes the "pulser" part way more complex.
Other advantage is, one ignitor type may easily serve wide range of lamps, the only limits are the maximum arc current (as it has to pass the HV transformer secondary in the ignitor, but usually the rating uses to cover rather high currents) and the peak voltage it generates (so if it is "HPS only" with its 1.5..2.5kV range or "HPS and MH" with its 3.5..5kV range). So with just barely 2 models you may cover practically all range of lamp types in use. However the ignitor type is quite tied to the operating voltages (ballast OCV and arc voltages), but for 230V series choke markets this is not any issue, as the OCV is 230V and the arc voltages in the 70..140V range everywhere. This simplified logistics (2 ignitor types are good for dozens of lamp types) is the reason why it is the primary choice in the "230V all series choke" (Europe,...) markets, even when it is a bit more complex (it needs its own transformer...) than other types.
In the "115V" markets (North America,...), because there the lamp arc voltages vary a lot (mainly the HPS), so essentially each lamp type would require a dedicated ignitor type, so their a bit higher cost makes them way less popular (till virtually non existent) there.
Compare to that there are "semiparallel" ignitors, which are in fact a LV pulsers connected to a tap of the main ballast, using the ballast winding as the HV pulse transformer. Because the main ballast winding is a low frequency coil, this means the HV pulses could be rather wide and slow, so tolerant towards higher capacitance (so longer cable) of the connection towards the lamp. Plus the ignition energy is greater, which may help with ignition of some lamps. But the drawbacks are, because the main ballast is part of the ignitor functionality, it has to be integrated together with it and the main ballast winding gets exposed to the high voltage. Because it uses the main ballast winding in function of the HV transformer, it is cheaper to make, so became the main choice whhat is used inside of the North American pulse start ballasts. In
And to complete the list. there are "parallel" ignitors, which are 2-wire devices connected just plain parallel to the lamp. These are simple to connect, but must generate all the ignition voltage inside of them, plus expose the ballast to the ignition voltage as well. On the other hand there is no component exposed to the arc current during the runtime, it becomes quite handy for really high power lamps (700W and above), mainly when many of these use to suffice with lower striking voltages (because the rather low buffer gas pressures). This type is used mainly when low ignition voltage is sufficient, or where the ignitor output power has to be rather high (to warm up electrodes in cold cathode mode), mainly with LPS lamps.