(NOTES from Reuven Hammer)
The original requirement at Hanukkah is "one light for a man and his household" (Shabbat 21b). But according to the School of Shammai, "Those who are zealous light one for each person and the extremely zealous light eight on the first eve and reduce the number thereafter." Yet the School of Hillel teaches that an individual lights one the first night and progressively increase them."
Modern Jewry has adopted the custom of the latter, which has to do with increase: an increase of the miracle of the oil for 8 days; an increase of the blessing of the light which dispels the darkness; and in increase of the light of the soul as the embers are stoked & kindled through faith & trust, and obedience & study, which causes it to burn brighter and brighter illuminating the darkness around us.
Hanukkah commemorates the struggle for religious freedom. The Maccabean revolt against the Seleucids was brought about by the fact that these Syrian Greeks forced observant Jews to abandon their religion and violate the Torah, the religious constitution of the Jewish People.
This is stated explicitly in the Hanukkah prayer Al Hanissim, "They demanded that we abandon YOUR Torah and violate YOUR mitzvot." For the first time, unfortunately not the last time, Jews were martyred because they attempted to observe the mitzvot of Judaism. Hellenism was not being offered as a choice, but as a coercive substitute for Judaism. (MY NOTE: The modern day form of Hellenism is Humanism – man is himself a god, therefore there is no need for any form of religion. Among humanists, religion only sparks hatred and disunity between civilizations.)
The light we kindle symbolizes the light of God's presence, the light that Torah brings into the world with its message of religious freedom.
This symbolism is found throughout Torah:
(Bereshit = Gen.1:3) Hashem's first utterance, "Let there be light!"
(Devarim = Exodus 3:2) The divine presence was revealed in the flames of the burning bush.
(Devarim = Exodus 19:18) And again in the fire at Sinai.
(Devarim = Exodus 27:20-21) Lights were kindled on the Menorah every evening in the Sanctuary to illuminate the ark.
(Mishlei = Proverbs 6:23) "The 'mitzvah' is a flame, and the Torah is light!"
(Zechariah 4:6) The Haftorah which describes the Menorah and then give its meaning: "Not by might, nor by power, but by My spirit says the L-rd of Hosts!"