Hannukah is to a year what Tikkun Hatzot is to a day. In the depths of the darkness we remember the deepest light of the world, the light of the Holy Temple, the revelation of the Highest in the lowest. (God in this world)
Rebbe Natan explains that the first mitzwah given to the Nation of Israel is the mitzwah of [seeking and] proclaiming the new moon is (Likkutei Halachot, very begining) because that is the essential purpose of the Jew, to seek out the spark of light in the darkness.
When we proclaim the new moon, the new month, Rosh Hodesh, the Mishnah [Rosh HaShanah 2:4] describes what that used to be like: They would light fires on the hilltops to signal to those far away that the new moon had been seen and the new month had begin. Rosh Hodesh is a very holy celebration we have each and every month.There were huge feasts and celebrations in the Temple each Rosh Hodesh.
When the signal fire reached the tallest hilltop visible to all those Jewish communities outside of the land of Israel they would wave the fire back and forth up and down until they saw answering fires throughout the exile. (throughout the rest of the surrounding countries) The words used are beautiful: They would wave the fire back and forth until the whole exile was alight like one giant bonfire. Think about that imagery: one little light, waving until the whole world seems to be filled with a roaring answering flame.
One little candle waving until the whole world is alight with the revelation of Godliness.
That's every mitzwah, as we are taught, נר מצוה ותורה אור, a mitzwah is a candle.
That's what it means to be a Jew. To seek out that little bit of light, in every occasion, in every place, in every person and wave that little spark of a candle until the whole world is going up, alight in the flames of Godliness.