Hanukkah, the eight day holiday of lights, is the simplest and most complicated of holidays all at once, and it functions in America in ways that would have been very impossible to predict from its history.
On the most basic level the traditional practice is to light a hannukiah (or menorah) at sundown on each of the eight nights of the holiday. The hanukkiah is placed in a window or some other public place so that the miracle can be publicized (which miracle? We’ll get back to that). People will also spin a dreidel and eat foods fried in oil. Of course, people exchange gifts, large and small with their loved ones as well. For reasons that have far more to do with its coincidental occurrence with Christmas, it also has a huge pop-culture footprint – check out for instance, the (dare I say – classic?) Adam Sandler Hanukkah Song or the menorahsaur I got for my kids.
On a historical level, the holiday is a celebration of the victory of Jews over their Syrian Greek conquerors in 164 BCE. In the ancient world, the Greek empire brought modernizing ideas and institutions to the Middle East, and in the land of Israel, many Jews embraced these developments. The Greek empire had one central idea: the creation of an advanced universal culture. Traditional Jewish culture had its own central idea: the idea of one true God. Jewish reformers wanted to merge these two ideas, so they assimilated parts of Greek culture into their own, taking Greek names like Jason, exercising in the gymnasium and prospering within Greek institutions. But not all Jews assimilated. Some resisted quietly, practicing and learning Torah in secret, while others fled to the hills and waged their own form of cultural resistance, which the Greeks were happy to ignore.
After a few years though, the spirit of toleration ended for unknown reasons. The Syrian Greek king, Antiochus IV, issued a series of decrees defiling the Jewish Temple and banning Jewish practice under penalty of death. Mattathias, the head of a priestly family and his five sons, led by Judah Maccabee, led an insurgent revolt against the regime. They fought against the Greeks occupiers and the Jewish reformers with equal ferocity. Ultimately, and perhaps miraculously, the small group of rebels did defeat the Empire. (and yes, Star Wars analogies are entirely appropriate here.)
So we return to the question -- What's the miracle? In some ways, the miracle was the victory of the tiny band of guerillas insurgents against the hegemonic Greek empire. But the later rabbinic tradition, which formed Judaism as we know it, focused not on the political miracle, but on a spiritual one – when the Macacabees regained control of the Temple they cleaned and purified it, but there was only enough oil to light the ritual candelabrum for one night.
That little cruse of oil miraculously lasted eight days, hence eight days of Hannukah. So you can choose between the military miracle or the spiritual one.
On a personal level, Hanukkah can be challenging. The heroes of the story can be seen as religious freedom fighters and a model for many liberation movements which have followed. However, this revolution, like many others, reserved its greatest fury for those who sought compromise, in this case between the Greek and Jewish cultures. Which is strange, since American Hannukah, is nothing if not an attempt to strike a compromise between Jewish culture and surrounding American culture. In a traditional Jewish framework, Hanukkah is actually a relatively minor holiday, perhaps like Arbor Day in an American context. It has become major only because of its proximity to Christmas in the Christian calendar.
Countless Jewish children see the beautiful lights and trees of Christian friends and neighbors and ask, “Where are our lights?” It is to answer that question, the hannukiah (or menorah) has become the major symbol we know today. See this article for more on the social history of Hannukah, if you're interested.
As a liberal American rabbi, who proudly and deliberately draws on my American heritage for some things, such as notions of individual liberty and gender equity and my Jewish heritage for others, such as a focus on the Divine, collective concern for the poor and the importance of spiritual practice, I see the power of learning from multiple heritages. That means I might well have been one of the Hellenized Jews who the Macabees sought to destroy. When I light my menorah, the heroes I will think of will be yes, the warrior Maccabees who resisted oppression, but even more so, the rabbis who 500 years after the Macabee revolt, retold the story and shifted the emphasis to the spiritual miracle of unwarranted hope and the oil which lasted for eight days. They inherited a story of military victory and re-imagined it, holding onto the past with one hand and the present with the other, so as to live a Judaism that was both authentic and meaningful.