"There is much rabbinic discussion of the connection between women's role and the mitzvah of lighting candles.
The act is seen as one of tikun olam, "repairing the world" and illuminating it.
Furthermore, Shabbat itself, and the Sabbath night in particular, are seen as inherently related to the role and nature of women.
The night of Shabbat is the time of the exaltation of the Shekhinah—God's indwelling Presence in the world.
The Shekhinah grows stronger on Shabbat, its light is more evident, and it turns routine household activities such as eating, drinking, and sleeping into sacred acts.
Woman is the eternal symbol of the Shekhinah.
The Shabbat hymns, such as Lekha Dodi; the Shabbat evening service; Kiddush; and the laudatory passage from Proverbs, "A Woman of Valor," recited at the Friday night table, are all replete with imagery linking Shabbat, the Shekhinah, and women.
Each verse and each custom enfolds and unfolds additional levels of association.
It also expresses the essence of Shabbat itself, the penetration of the light of this special day into mundane reality."
--Rabbi Adin Steinsaltz
From Teshuvah by Rabbi Adin Steinsaltz