All Jewish Holidays begin the evening before the date specified on most calendars. This is because a Jewish "day" begins at sunset and ends at nightfall, since it says in Genesis Ch. 1: "And there was evening, and there was morning, one day."
Work is not permitted on Rosh Hashanah, on Yom Kippur, on the first and second days of Sukkot, on Shemini Atzeret, on Simchat Torah, on Shavu'ot, and the first, second, seventh and eighth days of Passover. The "work" prohibited on those holidays is the same as that prohibited on Shabbat, except that cooking, baking, transferring fire and carrying, all of which are forbidden on Shabbat, are permitted on holidays. When a holiday occurs on Shabbat, the full Shabbat restrictions are observed.
The three pilgrimage festivals of Passover, Shavuot (Feast of Weeks), and Sukkot (Festival of Booths) mark not only historical events in the development of the Jewish people like the Exodus from Egypt, the receiving of the Torah on Mt. Sinai, and G-d’s sheltering of the Israelites in the desert for 40 years, but also agricultural celebrations and the seasonal harvests in the Land of Israel.
The other holidays mentioned in the Torah are the High Holy Days: Rosh Hashana and Yom Kippur. In addition to that we celebrate the rabbinical holidays of Chanukah, commemorating the rededication of the Temple in Jerusalem after a group of Jewish scholars defeated the occupying Greek armies and Purim where the Jewish people were miraculously saved from the evil decree of Haman.