Like all others before and since, the struggles for Jewish survival that we commemorate on Chanukah and Purim had their military battlefields and their spiritual ones. But Chanukah and Purim were unique in one way: they allowed G-d’s celestial light to spread on a clear and unambiguous level, and to bring on some unique and vital rectifications.
On a military level, Chanukah commemorates the victory of the Hasmoneans (the band of virtuous Jewish loyalists headed by Judah Macabbee, the Kohen) over Antiochus (the Syrian leader of the Greek forces), while Purim concentrates on Mordechai’s bold defeat of the wicked Haman’s followers.
But on a spiritual level Purim came down to a battle for the preservation of the Jewish Nation, while Chanukah focused on the fight to withstand the forces of assimilation. For Haman and his cohorts wanted to destroy the Jews en masse, while the Syrian-Greeks wanted to have them merge into Greek culture and abandon the Torah.
With G-d’s help, the Hasmoneans managed to defeat the forces of assimilation and to bolster Torah observance. And they did that by drawing upon the holiness of the Menorah in the newly-reconsecrated Temple (the site of the miraculous flask of oil that stayed lit for eight days), which was emblematic of the emanation of G-d’s light in the world.
And Mordechai and Esther managed to thwart Haman’s wicked plans to destroy us. By drawing upon the light that emanates from G-d’s Torah they also inspired us to bolster our observance of it and to reaffirm our commitment to it from that time onward.
Since the miracles and victories of both Chanukah and Purim are rooted In G-d’s emanations, all the mitzvot associated with them are thus either directly or indirectly pertinent to light (E.g., lighting the Chanukah menorah, expressing the “light, gladness, joy, and honor” [Esther 8:16] of Purim), or to emanation and bestowance (E.g., the giving of gifts to friends and others on both occasions, the Purim feast).