The victory over the Syrian-Greeks, the resultant rededication of the Temple, and the miracle of the oil.
The Seleucids (Syrian-Greeks) under Antiochus Epiphanes (2nd century BCE), at the instigation of the Hellenizers, had forbidden various Torah-practices, such as Sabbath-observance, and pressed the Jews to offer up idolatrous sacrifices. The Hasmoneans (a family of religious Jews) fought to retake the Holy Temple, which had been seized by the Seleucids, and to enable the people to once again observe the Torah. When they reached the Temple grounds, they found only one day's supply of unsullied olive oil, but the oil lamps miraculously burned for eight days (Talmud, Shabbat 21b), allowing enough time for new oil to be prepared and brought.
The significance of the miracle is that it demonstrated that God's presence still dwelt in the Holy Temple.
The Torah Sages instituted the festival of Hanukkah at that time (Talmud, Shabbat 21b), to publicize the miracle (Rashi commentary, ibid). The eight-day rededication of the Temple is also mentioned in the book of Maccabees (I, 4:36; and II, 1:18); and Josephus mentions the eight-day festival in Antiquities ch.12.
The Al-Hanisim prayer which we recite during Hanukkah centers around the Hasmoneans' victory, while the candle-lighting commemorates the miracle of the oil.
Though the military victory is prominently mentioned in the prayers, it wouldn't have been celebrated if not for the miracle of the oil.
It should also be noted that the main goal for which the Maccabees fought was not political independence. They fought to enable the people to observe the Torah's commandments; as we say in the Al Hanisim prayer: "the Greeks sought to cause us to forget Your Torah and leave Your statutes."
Hanukkah is a Jewish celebration:http://judaism.answers.com/jewish-holidays/hanukkah
Only the Jews in Mexico celebrate Hanukkah.
Jewish people who live in England celebrate Hanukkah.
Yes, most Jewish people celebrate Hanukkah.
Almost all Jews celebrate Hanukkah.
French Christians celebrate Christmas. French Jews celebrate Hanukkah.
Jews around the world celebrate Hanukkah, including in Israel.
Jewish people celebrate Hanukkah. (They are not called "Hanukkah people")
Yes, Jews celebrate Hanukkah in many different countries.
Yes, the small Jewish minorities in the African countries celebrate Hanukkah privately in their homes.
They don't. Jews believe that Jews should celebrate Hanukkah.
Hanukkah is a Jewish celebration with no connection to Buddhism.