The Story of Hanukah
In 167 BCE the Greeks, led by Antiochus, issued decrees forbidding Jewish religious practice. They tried to eradicate the Jewish religion by killing all who showed any reluctance in worshiping the Greek gods. They forced the Jews to sacrifice unclean animals (pigs, for example) on their altars, and they desecrated copies of the Torah and any other symbols of Judaism.
Some Jews fled into the wilderness, led by the Chasidim. They mounted a campaign of guerrilla warfare. Somehow, after many battles, they finally managed to push back the Greeks. A turning point in the war was when the Jewish leader Mattathias decided that it was okay for the Jews to defend themselves on the Sabbath. This was a very religious war.
When the Jews, led by Mattathias' son Judah Maccabee, finally retook Jerusalem, they cleaned out the temple and lit the menorah. (This was The Menorah, designed as dictated in Exodus 25:31-40) But there was only one undesecrated cruse of oil, enough to last for one day. It would take eight days for the priest to prepare more oil that was untouched by pagan hands.
The one cruse lasted eight days. This was clearly a miracle, and is the reason for Hanukah.
The Celebration of Hanukah
Hanukah starts on the 25th day of Kislev of the Hebrew calendar. This floats around on the Gregorian calendar, falling sometime in November or Decenber. Hanukah lasts for eight days during which lamentation for the dead and fasting are forbidden. Other than that life goes on as normal during Hanukah, aside from the lighting of candles and general celebratory atmosphere. It is not usual to take off from work during Hanukah.
The primary religious tradition of Hanukah is the lighting of the menorah, AKA the hanukiah. The candles are lit at sundown and left to burn for at least half an hour, and usually left until they burn out on their own. The menorah should be placed so that the light of the candles can be seen by neighbors and passersby.
There are also some traditional foods eaten at Hanukah -- latkes (potato pancakes), apple sauce, beef brisket, and jelly donuts (sufganiyah) for desserts and snacks.
It is traditional to play with a dreidel (sevivon), a spinning top that is used as a type of four-sided die in a simple gambling game. It is also common to give small gifts, especially to children, during Hanukah. This tradition is becoming even more popular as Hanukah tries to become a stand-in for Christmas.
Because the 'real' name for Hanukah is written in Hebrew there are many ways to translate it into English. Other common English spellings include Hanukkah and Chanukkah. It is also known as the Festival of Lights.