The events of Chanukah took place around 150 years after the death of Alexander of Macedonia. After his death, the Greek empire was divided into four parts; Israel lay squarely between the Ptolemaic branch in Egypt and the Seleucid, based in Syria.
Although Alexander the Great himself was a friend to the Jews, his conquest of the world brought about the global spread of Hellenistic civilization
. Greek culture, though rich in areas of art, literature, philosophy, mathematics, and science, was antithical to Jewish Torah values in many ways - the philosophies of hedonism, cynicism, and epicureanism, the glorification of the human body, sexual depravity, and the worship of pagan gods - to name a few. Despite some inroads by the Hellenists, many Jews were able to withstand the pressure and stay true to their heritage until the time of Antiochus IV Epiphanes
Evil King Antiochus persecuted the Jews, and set harsh decrees against them, forbidding: Brit Milah, Shabbat, declaration of the new moon, and Torah learning (those things that made Jews unique in body, time and thought). He decimated Jerusalem and set up idols in the Beit HaMikdash (Temple).
In the city of Modi'in, the Greeks set up an idol of Zeus and asked the local populace to sacrifice a pig to it. When a Jewish Hellenist stepped forward to comply, an eldery Kohen (actually the rightful Kohen Gadol) named Matisyahu (Matthias) of the family of the Hashmona'im, came forward and killed him. He rallied the people to his side with the cry "Mi Kamocha baElim Hashem" (who is like You among the mighty ones, oh God!) and the acronym of those words - Maccabee - became the name of the rebels.
Despite facing an overwhelming number of trained, professional soldiers, the Maccabim (Maccabees), led by Matisyahu's 5 sons, were successful in battle after battle, until they were able to recapture the city of Jerusalem itself.
The victorious soldiers cleared out the Temple, but found only one small cruse of oil that had not been contaminated. A miracle occured, and the oil lasted for 8 days (either till they were able to send messengers to Tekoa, a four-days journey, to get oil and return; or 7 days for the process of ritual purity from contact with the dead and another day to process the oil).
To "publicize the miracle", each member of each household lights a Menorah each of the eight nights of Chanukah. The candles must burn for at least half an hour after sunset - which, in times before electricity, was when people were still found in the streets. (Per my Rabbi, I let my Menorah stay alight much longer since people are out and about much later these days.) The best way to perform the Mitzvah is with olive oil, though any kind of flame-producing candles are kosher as well. We light one lamp the first night and progressively add one more each night. The Menorah is best placed to the left of the doorway, so that we are surrounded by Mitzvot (the Mezuza being on the right doorpost. After lighting, the family sings Ma'oz Tzur