The word Chanukah means to dedicate. The Assyrian Greeks had taken control of the land of Israel and were imposing decrees upon the Jewish people that were becoming intolerable. The Greeks wanted to "enlighten" the Jewish people with their way of looking at the world. When the Jews rejected this way of life, the Greeks began to make decrees on the Jewish people to break their spirit such as denying the the chance to perform bris milah on their sons, or from keeping Shabbat, or from making their calendar.
When this did not stop the Jewish people from leaving their faith (some did), the Greeks attacked the symbol of Jewish wisdom and pride, the holy temple in Jerusalem.
After rousting the Greek army from the temple, the priests of that time entered the temple and rededicated it to G-d, (Chanukah) and found a little kosher olive oil left with the high priests seal to last for one day, which miraculously lasted for eight days.