It commemorates the cleansing of the second Temple in Jerusalem after it had been defiled.
Antiochus IV had sacrificed a pig on the altar in 167 B.C. Of course, this defiled the Temple.
This evil Seleucid ruler ( modern Afghanistan, Iran, Iraq, Syria, and Lebanon, together with parts of Turkey, Armenia, Turkmenistan, Uzbekistan, and Tajikistan) persecuted the Jewish people. In just four days he murdered and made 80,000 Jews homeless!
Zeus was the false god of the sky and ruler of the Olympian gods to which the sacrifice had been made.
But . . . only three years later (164 B.C.) Antiochus suddenly died of a strange disease. So much for those who persecute God's people, the Jews!
In John 10:22 Hanukkah is referred to as the "Feast of Dedication".
The Maccabees, of course, liberated the Temple. In the Temple there was only a very small cruse of consecrated oil.
But the miracle of Hanukkah is that this small amount of oil continued burning for eight days. This gave the priests time to consecrate more oil to keep the fire burning.
Today Jewish people celebrate Hanukkah with sufganiyot (jelly doughnuts), gelt (money), potato latkes (pancakes), and dreidels (spinning tops).
Recipes to make all 8 nights of Hanukkah delicious: http://www.huffingtonpost.com/2013/11/22/hanukkah-recipes_n_4319481.html