The Gemara asks the following question: ” Mai Chanukah, What is Chanukah”?
Rashi explains the Gemara’s question to mean, “Due to which miracle was the Yom Tov of Chanukah instituted?”
The Gemara goes on to answer the question as follows: On the 25th day of Kislev begin the eight days of Chanukah. It is prohibited to eulogize anyone on these days and it is prohibited to fast on these days.
Why?
When the Greeks entered the Bais HaMikdash they[handled all the vessels and touched and] made all the oil [that was used to light the menorah] impure. When the Chashmonaim (sometimes referred to as the macabees) overpowered the Greek army and won the war they searched the entire Bais HaMikdash and were only able to find one small jug of pure oil [with the seal of the Kohen Gadol on it].
There was only enough oil in this jug to light the menorah for one day. However, a miracle occurred and the small amount of oil was sufficient to light the menorah for eight days (until they were once again able to purify themselves and produce more oil).
The following year, beginning on 25 Kislev, the Chachamim instituted an eight day Yom Tov (which we refer to as Chanukah) dedicated to Halel (praise) and Hoda’ah (Thanks) [to Hashem].
(Talmud Shabbos 21b, also brought in the Tur beginning of Hilchos Chanukah)
1) According to many Rishonim there is no requirement to have a Seudah (festive meal) on Chanukah, and any Seudah that is made is a Seudas Reshus (non obligatory meal).
Others argue and maintain that there is indeed a requirement to have a Seudah, with bread, on Chanukah.
The prevelant minhag when having a Seudah on Chanukah is to sing Shiros V’Tishbachos (praises) to Hashem and/or talk Divrei Torah, thus making it a Seudas Mitzvah according to all opinions.
2) It is customary to eat foods made with cheese on Chanukah in commemoration of the miracle of Yehudis’ slaying of the Greek general Heliphornius which is considered one of the miracles of Chanukah, in which cheese played a role. (See Ram”a Siman 670:2 and Mishna Berura S”K 10. for more on the story. )
(from Halachos for Today)