How many festivals are there in Judaism and what are they?
There are three principle Torah festivals. There are Pesach (Passover, the time when the Jewish People were redeemed from Egypt, and became a nation), Shavuos (Pentecost, the time when the Jewish People received the Torah), and Sukkos (Tabernacles, in memory of the Jewish People’s journeying through the wilderness).
In addition, the days of Rosh Hashanah (the New Year) and Yom Kippur (Day of Atonement) are different types of festivals. They are days of joy, for they are days of closeness with God, yet their mood is somber, for they are days of crucial judgment.
Formally, Rosh Chodesh (the New Month) is also a festival, yet its commemoration as such cannot be compared with the commemorations of full Torah festivals.
There are two rabbinic festival days, which were enacted by the Sages: Purim, commemorating the (hidden) miracle that saved the Jewish People from the decree of Haman, and Hanukah, commemorating the defeat of the Greeks by the Maccabees, and the miracle of the oil that accompanied it.