Unlike Christmas, Hannukah is a holiday that Jesus himself celebrated:
They were celebrating Hanukkah just then in Jerusalem. It was winter. Jesus was strolling in the Temple across Solomon's Porch. Several Jews, circling him, said, "How long are you going to keep us guessing? If you're the Messiah, tell us plainly."
-John's Gospel
Hanukkah is a celebration in remembrance of a successful Jewish victory fighting off a powerful Greek oppressor, and the successive rededicating of the Temple in Jerusalem to God, all this occurring about 200 years before Jesus the Messiah was born.
A Greek general by the name of Antiochus Epiphanes conquerored Israel, destroyed much of Jerusalem, cruelly put many Jews to death, setup a altar to Zeus inside the Temple in Jerusalem, and sacrificed a pig on the altar to Zeus.
In response, a Jewish revolt led by Judah Maccabee fought off the Greek oppressors. The Maccabee group then cleansed the Temple, restored it, and re-dedicated it to God, thus becoming the first Feast of Dedication, the first Hanukkah.
It is a time to rededicate yourself to God, and remember how God helps his people even in the hardest times. This Messianic psalm by Marty Goetz is a beautiful musical piece of what Hanukkah is about.
Happy Hanukkah!