Seven symbolizes the Natural order, for G-d created the world in six days and rested on the seventh; Shabbos. Eight, symbolizes the Super-natural. The Human intelligence is limited to the Natural order; anything which is above and beyond Nature is also above and beyond human understanding. G-d, is obviously over and above Nature. We therefore cannot understand G-d, or his ways.
The Torah and Mitzvoth, which contain G-d's wisdom and will, are also beyond our understanding, but the more Torah we learn and the more Mitzvoth we observe, the more we become attached to G-d.. By being attached to G-d, we are no longer limited to our OWN human resources, but are now able to draw from the unlimited of G-d's wisdom.
At the time of Chanukah, the Jewish people were challenged to this view and way of life. The Greek philosophers believed that there was nothing higher than the human intelligence. They did not believe in the true G-d, the Creator, because they did not understand G-d, and according to them, anything that could not be understood was not to be believed.
King Antiochus wanted to force the Jews to give up the Mitzvoth which seemed "unreasonable" to him. Like the Mitzvah of the Bris which is done on the eighth day. Antiochus had vast armies, ready to put to death any Jew who disobeyed his orders, which now put the whole future of the Jewish people in great danger. Fortunately, a handful of Jews, led by Mattisyohu and his sons, openly resisted Antiochus. They kindled the flame of true faith in G-d, and with G-d's help they were victorious for they would not compromise with the enemy.
The miraculous victory of the Jews against the Greeks was not only in the battlefield, but a great spiritual victory, the victory of light over darkness. And the one little cruse of pure olive oil, miraculously lasted for eight days, instead of one.
The eight Chanukah lights, reminds us that the true approach to Torah and Mitzvoth is not through the limited human intelligence, but rather through the actual fulfillment of the Mitzvoth first and foremost.