Like many Jewish holidays, Hanukkah has several different legacies and meanings, which can be accentuated or played down, depending on one's religious convictions.
First and foremost, Hanukkah is a historical, nationalist holiday. It commemorates the successful rebellion, in the second century B.C.E., of a clan of Jewish freedom fighters called the Maccabees. These warriors rose up against Antiochus, a Greco-Syrian monarch who ruled Israel with a hard hand, banning Jews from practicing their faith and pressuring them to convert to a Hellenic way of life. (It is told that his soldiers would even force-feed Jews pork, a kosher no-no.) Despite being greatly outnumbered, the Maccabees managed to recapture the Holy Temple, the premier site of ancient Judaism, from their oppressors. Hanukkah means dedication in Hebrew -- the holiday pays tribute to the dedication of a group of Jews who believed fervently in their right to religious and nationalist freedom.
Of course, there's also a religious aspect to Hanukkah. Also known as the "Festival of Lights," Hanukkah celebrates the miracle that occurred when the Maccabees reclaimed the Temple. The sanctuary was a shambles, torn apart by the Hellenic forces. The fighters found only enough oil to light a lantern -- by which to read the Torah -- for one day. But the lantern blazed for eight full days. When Jews light the eight candles of the menorah on the eight nights of Hanukkah, they recite a prayer extolling God who "performed miracles for our ancestors in days of old."
There is also a seasonal, even pagan, aspect to Hanukkah. Celebrated on the 25th day of the Jewish month of Kislev, during the darkest days of the year, the candle-lighting holiday is a warm, cozy ritual to banish the winter blahs. The focus of the holiday is not so much going to synagogue or reading certain scriptures, but rather staying at home with friends and family, eating, playing, and just spending time together.
In the U.S., where Santa Claus rules the month of December, some Jews have incorporated a little bit of Christmas into their Hanukkah spirit. Some families opt to give gifts each night of Hanukkah; others may decorate their house with a "Hanukkah bush." Even though the two holidays have vastly different religious and historical origins and focus, both Christmas and Hanukkah are a beautiful opportunity to open up one's house and heart and spread some joy.