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.
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.
In addition to the famous shtikel from the Mishnah Berurah mentioned above, the Machatzis Hashekel adds:
ועיין בט"ז שכ' מ"ש לעולם יסדר כו' ר"ל דרך קביעות סעודה בפריסת מפה ועריכת שלחן והדלקת נרות כמו בליל שבת ועמש"ל סי' רצ"א בע"ה
So according to this view the candles are one element that constitutes a fixed meal and "set table", just like we have on Shabbos itself.