Major Jewish holidays in calendar order (the year starts with Rosh Hashanah, even though it’s the first and second day of the seventh month in our calendar – we’re weird that way ):
Rosh Hashanah - the Jewish New Year. Literal translation: Head of the Year. Two days (except that it’s one for Reform Jews worldwide and celebrated for two days in Israel but they are considered one forty-eight hour day - go know). Family get-togethers and meals, special services in synagogues. Traditional foods include round challah (to symbolize the circularity of the year and life) and apples and honey (for a sweet year). Many Jews who never go to shul/synagogue/services throughout the year go on Rosh Hashanah and Yom Kippur (known together as the High Holidays). A ram's horn instrument called a shofar is blown. Some traditional greetings: Chag Sameach (gutteral ch like loch, not like church), Gut Yomtov, L'shana tovah, Happy New Year. Occurs in September or October.
Yom Kippur - the day of atonement. A fast day – no food or drink from just before sundown until about an hour after sundown on the following day. An arcane and moving ritual called Kol Nidre in the evening, services pretty much all day during the next day. Group confessional and atonement - all the confessions are in the "we" form. Traditional to wear white, to not wear animal products, to wear a kittel (burial shroud). No traditional foods :-). In many congregations the only time Jews kneel and prostrate themselves, during the part of the service that remembers/reenacts the High Priest’s prayers in the Temple. There's a memorial service that's very moving, called Yizkor. Ends with the blowing of the shofar. "Have an easy fast," "Gut Yomtov" and "Happy New Year" are all good things to say. There are more specific ones in Hebrew, but maybe that's too much. It’s the tenth day of the year, counting the first day of Rosh Hashanah as the first.
Sukkot - lasts 7 days, and is immediately followed by Shemini Atzeret and Simchat Torah. Sukkot starts on the fifth day after Yom Kippur. So, it’s a big holiday season going from Rosh Hashanah through Simchat Torah. Jews build temporary huts called sukkot (plural of sukkah) and "dwell" in them (usually by having festive meals in them). Harvest holiday of biblical origin. USAmerican Thanksgiving is based on sukkot (them Puritans knew the bible). The last day is called Hoshanah Rabbah. Greeting: Chag Sameach (Happy Holiday in Hebrew), Gut Yomtov (Happy holiday in Yiddish), Happy Sukkot are all fine. Very fun to get invited to a sukkah. I don't have one of my own (because I live in an apartment with no outside space of my own) and love to go to other folks' sukkot.
Shemini Atzeret and Simchat Torah – For all Jews in Israel and the Reform movement worldwide, these are collapsed into one day, but for the rest of us they are two days, immediately following Sukkot. I sort of view Shemini Atzeret as the eighth day of Sukkot, which is probably not that accurate, but “Shemini” does mean “eight.” Simchat Torah is literally "joy of the torah" and it’s a very fun holiday. The Torah is the scroll version of the Five Books of Moses, the Pentateuch, the Humash (any of this ring a bell?): Genesis, Exodus, Leviticus, Numbers, Deuteronomy. The Jewish bible consists of Torah, Nevi'im (writings of the prophets), and K'tuvim (other stuff :-)). Very joyous. Processions with the Torah, dancing with the torah (and each other). Kind ofraucous. Say Chag Sameach - just keep saying it :-).
All of the above are fall holidays (in the northern hemisphere). No major holidays until spring:
Pesach - Passover in English. Festival of Freedom. Commemorates the Exodus from Egypt. Main feature is a ritual meal called the seder. Two seders the first two nights (lasts 8 days) except in Israel and as celebrated by Reform Jews worldwide (they do one seder, officially, and have a seven day holiday although certainly some Reform Jews have a second seder and why shouldn’t they since two seders are twice as fun). This is the holiday most celebrated by USAmerican Jews. Jews who never set foot in a shul often still go to a seder. The seder has prayers and readings from a book called the Haggadah. Lots of different haggadot, lots of opportunity to talk about different struggles for freedom. My favorite holiday. Lots of food restrictions, though. Traditional foods: matzo and assorted foods that meet the food restrictions (too complex for a short summary). Say Chag Sameach or Happy Passover.
Shavuot - another harvest holiday of biblical origin. Holiday of first fruits. Late spring. Lasts two days (one in Israel or if you're Reform). Also celebrates the 10 commandments. The cheesecake holiday! Dairy products are traditional.
A few not so major holidays:
There was a “Summary of Most Jewish Holidays” going round the ‘net a few years back.
1. They tried to kill us.
2. We won.
3. Let's eat
It came with recipes :-). It applies to Chanukah and Purim, and also the major holiday of Pesach.
Chanukah commemorates the Maccabean rebellion against Syrian occupation. The rebellion was led by a man known as Yehuda haMacabee (Judah the Hammer) and his brothers. It was an early guerilla war and they won over the larger and better equipped Syrian army. The descendants of the last surviving Macabee brother became the Hasmonean dynasty. The story is told in the books Maccabees 1 and 2, which are not part of the Jewish bible but are part of the Catholic bible. Life's funny. The Hanukah story was an historical event and has contemporaneous records, although certainly it got embellished in the retelling.
Chanukah lasts 8 days. A hanukiah or hanukah menorah (a nine-branch candleholder) is lit each night. One candle for each night plus a shamash (helper) candle that you light from. So 2 the first night (but one's the shamash), 3 the second. All lit the last night. Traditional foods: latkes (potato pancakes) and soofganiot (jelly donuts). Traditional to give children coins (real or chocolate) and in USAmerican households particularly, small gifts. Traditional game: dreidel (a spinning top with Hebrew letters on it). Occurs somewhere between late November and early January.
Purim - holiday based on the Book of Esther, last (and most controversial) book to be canonized in the Jewish bible. Tells how Esther, a crypto-Jew and the Queen of Persia, saves her people from total destruction. There's no historical basis for the story and the main characters (Mordechai and Esther) are thought by many to be derived, with much adjustment, from the Babylonian (?) gods Marduk and Ishtar. Traditional food: hamentaschen (three cornered yummy filled cookie). Traditional activities: dressing up in costume, giving small gifts of food to one's family and friends, donating money or food to the poor, reading the Megillat Esther (book of Esther) and making lots of noise when the villain's name (Haman) is read, and getting drunk. In the spring, a month before Pesach.
Tu B'shvat - New Year of the Trees. Hug a tree on that day. Minor holiday often used for ecologically positive messages and activities.
Tisha B'Av - anniversary of the destruction of the Temple. Very sad day. A fast day. In the middle of the summer, when it's hard to go without food or drink.
A personal family note: I'm one of six siblings and my baby sister and I are the most Jewishly involved of the bunch of us (interestingly, we are the only ones who intermarried as well). Our practices are not identical, but pretty compatible, and differ sharply from those of the rest of our sibs. I'm not sure why or how that happened, but in any event it's something we each chose as adults, not something we were raised with.
Our parents were secular Jews but felt children should be raised with religion, so they joined a Conservative shul (once we left North Dakota, where we were the only Jews in a 40-mile radius) and sent us to Hebrew School. They did celebrate shabbat (Sabbath) by lighting candles and with a special meal, and they did have seders and follow some food restrictions for Pesach, but neither of them could read Hebrew and neither of them had formal religious education. So most of what I know about Judaism in general and holidays in particular was learned at school and shul and through reading and adult education over the years, not at home growing up. In fact, it mostly went the other way when I was growing up. We'd come home from Hebrew School and say "We're supposed to do X" and sometimes we'd add that to our family practice. As a result, I used to think of people who observed the "summer holidays" of Shavuot and Tisha B'Av as really religious, since Hebrew School wasn't in session :-).