Hanukkah (חנוכה) is the a winter feast (usually in december) meant to celebrate the rededication of the temple. It is not mentioned in the bible, but Jesus celebrated it (John 10:22-24). It starts on the 25th day of the month of Kislev (according to the jewish calendar), and it is 8 days long.
Flavius Josephus (the Jewish Roman historian) retells the story of the background of Hanukkah1:
Before the Maccabean revolt against the Greek rulers (around 165 B.C.), the Seleucid king Antiochus IV Epiphanes had desecrated the temple by forcing people to worship the Greek gods and by sacrificing a pig on the altar. He also made the people abandon their worship of God, their holy customs and reading of the Torah.
As a result, a group of four Jewish brothers, led by Judah Maccabee, started a revolt. They were known for their strong faith and loyalty to God, and they fought for 3 years before they miraculously won and freed the land of Israel from the Greco-Syrian control.
After regaining the Temple, it was cleansed by the Maccabees, cleared of all Greek idolatry, and readied for rededicated. The rededication of the Temple to the Lord took place in the year 165 BC, on the 25th day of the Hebrew month called Kislev.2
This is why Hanukkah is called the Feast of Rededication. Another miracle gave it its second name, the Festival of Lights:
As a symbol of God’s presence in the Temple, the Menorah (מְנוֹרָה, the seven-branched lampstand) had to be lit at all time. But when the Temple was rededicated, there was only enough oil left for one day because the rest of the oil had been defiled by the Greeks during their invasion. The process of purification would take a week, which would have taken too long. So the Maccabees went ahead and lit the eternal flame with the remaining supply of oil, believing that it would stay lit. And it miraculously burned for eight days, until the new sacred oil was ready. That’s why the Hanukkah Menorah (Called Hanukiah חַנֻכִּיָּה) is lit for the eight nights of the celebration.3
Hanukkah appears in John 10:22-39, where some people came to Jesus asking him if he was the Messiah, the one to liberate them from the Roman oppression. They were hoping for a Messiah who, as an other Judah Maccabee, who would be raise an army up to free them from the Roman occupation. And Jesus confirmed that he really was the Messiah, but he also mentioned that they could not recognise him in his role of saviour because they were not his sheep (John 22:26). He came for the lost sheep of Israel, to bring them back to him, and for the gentiles. But he will come back to build an eternal kingdom, not a temporary one, just like Isaiah says:
For to us a child is born, to us a son is given; and the government shall be upon his shoulder, and his name shall be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. Of the increase of his government and of peace there will be no end, on the throne of David and over his kingdom, to establish it and to uphold it with justice and with righteousness from this time forth and forevermore. The zeal of the Lord of hosts will do this. (Isaiah 9:6-7)
The Hanukiah has 9 branches, 8 for each day, while the 9th one is considered called the servant (Shamash) used to light the other ones:
The eight candles receive their light from the one. Its role is to serve. The […] Shamash can be regarded as a visual symbol of Jesus, who gives light to all who allow themselves to shine for God. He said of himself, “the Son of Man did not come to be served, but to serve, and to give His life as a ransom for many.” (Matthew 20:28)4
John says that Jesus is the true light, “…that gives light to every man.” (John 1:9) And he was probably quoting Isaiah, whose prophecy states:
The people who walked in darkness have seen a great light; those who dwelt in a land of deep darkness, on them has light shone. (Isaiah 9:2)
Later on in the same chapter, Isaiah mentions the birth of Messiah (Isaiah 9:6-7). And Hanukkah is celebrated around the time of Christmas, the celebration of Jesus’ birth. Jesus talked about himself as the temple: “Destroy this temple, and I will raise it again in three days.” (John 2:19) Similarly, Hanukkah celebrates the temple of God being raised again, rededicated to celebrate our Father.
A Hanukiah (חַנֻכִּיָּה, nine-branched lampstand) is lit during the festival. A first light is usually lit using the Shamash on the first day as sunset, an additional one on the second day, and so forth. Rabbinic law (through tradition) states that the lights should remain lit for at least half an hour per evening. Additionally, three blessings are usually said over the lights. On the first day, all three are said, while on the consecutive days, only the first two are recited.5 After the lighting of the candles, the song Ma’oz Tzur is sung. Interestingly, the first verse mentions the rock of salvation6, where salvation (יְשׁוּעָ, Yeshua) corresponds to Jesus’ name in Hebrew. Sometimes, Psalms 30, 67, and 91 are recited.
Fried food is usually eaten to remember the importance of the oil that was burning in the temple.
Wikipedia additionally states7:
The last day of Hanukkah is known as Zot Hanukkah, from the verse read on this day in the synagogue (Numbers 7:84, Zot Chanukat Hamizbe’ach, “This was the dedication of the altar”). According to the teachings of Kabbalah (Mystic Judaism) and Hasidim (Orthodox Judaism), this day is the final “seal” of the High Holiday season of Yom Kippur, and is considered a time to repent out of love for God. In this spirit, many Hasidic Jews wish each other Gmar chatimah tovah (“may you be sealed totally for good”), a traditional greeting for the Yom Kippur season.
1 Flavius Josephus, Book of Jewish Antiquities, Book 12, chapters 5-7 (Online)
2 Article on About.com
3 Article on JewsForJesus, and Flavius Josephus, Book of Jewish Antiquities 12:325 (Online)
4 Article on JewsForJesus
5 Shulkhan Arukh Orach Chayim 676:1–2; Transliteration of the prayers
6 Translation of the Ma’oz Tzur
7 Article on Wikipedia
8 De Noon, Steven; Hanukkah holds the Mystery of Messiah