I have seen different Minhagim regarding lighting one or two candles on Motzei Shabbos. What is the source and why 1 or 2?
Commenting on the Shulchan Aruch's "One should always set his table on motzae Shabas to escort Shabas", Mishna B'rura 300:3 writes:
And for the same reason, some are accustomed to having more lamps on motzae Shabas than during the week, and also are accustomed to saying poems and songs after havdala.
I seem to recall that they are also "neshamah licht" (candles in memory of the departed) for King David, who died on Shabbos afternoon (and who is associated with the melaveh malkah meal).
My mother has the custom of leaving two candles lit, either which were the actual ones used for Havdalah or lit from the Havdalah candle. Her mother called them "Shulem Bayis Lichten". I do not yet know of a written source, but with minhagim I believe that a mimetic source should suffice. (Minhag Yisrael Torah)
As far as the reasons, I have theories. However, I think anyone else's guess is as good as mine.
My Rebbi told me it is because just as we escort shabbos in with light, so to do we escort it out with light. I've always seen the minhag with 2 candles.