The Eight days of the festival of Chanukah begin on the twenty-fifth of Kislev. Lights are kindled every evening for the eight days of the holiday.

The Sages (Shabbat 21b) asked: What is Chanukah? The Rabbis taught: From the twenty-fifth day of Kislev, eight days of Chanukah are observed, during which eulogies are not made and fasting is not permitted. For when the Greeks entered the Sanctuary, they defiled all of the oils [used for kindling the Menorah]. And when the Hasmonean House prevailed and defeated them, they searched and found only one jar of oil which was sealed with the seal of the Kohen Gadol – and this jar had oil sufficient only to burn for one day. But a miracle occurred and the oil burned for eight days.

The next year, the Sages designated these eight days as a festival, with songs of praise and thanksgiving. During the period of the second Holy Temple, the Greek kings issued harsh decrees against Israel, outlawing their religious practices and forbidding them to engage in the study of Torah and the practice of mitzvot. They stole their money and their daughters, entered the Sanctuary and ravaged it, defiling all that was ritually pure. They caused Israel great anguish and oppressed them until the G‑d of our fathers had mercy upon them and delivered them and saved them from the hands of their enemies. The Hasmonean House – the Kohanim Gedolim – prevailed and killed them and saved Israel from their hands. And they designated a king from among the kohanim, and the kingdom of Israel was restored for more than two hundred years, until the destruction of the second Holy Temple.

It was on the twenty-fifth day of the month of Kislev that Israel prevailed and defeated their enemies. They entered the Sanctuary and found only one jar [of oil] which was pure. It contained only enough for one day, but they lit the lights of the Menorah from it for eight days, until they pressed olives and extracted pure oil (Rambam, Hilchot Chanukah 3).

The Sages of that generation therefore decreed that these eight days, beginning with the twenty-fifth of Kislev, be designated days of rejoicing and praise, and that lights be lit at the entrance to homes on each of these eight nights, to publicize the miracle. And these days are to be called Chanukah – [inauguration, consecration; one could also interpret the word as] chanu [they rested] kah [on the twenty-fifth] – for on the twenty-fifth they rested from the battle with their enemies.

The Talmud (op. cit.) states that the days were designated for "praise and thanksgiving." We fulfill the obligation of "praise" by reciting the complete Hallel during Shacharit, the morning prayers on all eight days of Chanukah. The obligation of "thanksgiving" is fulfilled by reciting Al haNissim which is inserted into the Amidah prayer and the Grace after Meals.