Jewish Holidays span the entire Jewish calendar. Most of the Jewish holidays come straight out of the Bible. Later on, Rabbis added more holidays.
Passover in the Spring
In the springtime, Jews celebrate Passover. 49 days later, they celebrate the giving of The Covenant, The Bible at Mt. Sinai.
In the fall, generally between September and October, the Jewish people around the world celebrate the Jewish New Year. 10 days later, the Holiest day on the calendar, they observe The Day of Atonement. On that day, adults fast for an entire 24+ hour period and repent for their iniquities. The 10 day period is known as the High Holidays.
A mere 4 days later, Jews celebrate the Holiday of Sukkot and sit in small temporary huts. This commemorates the Jews travelling in the desert to the Promised Land.
Perhaps the most famous (and most commercialized) Jewish Holiday is Hannukah. It is not even mentioned in the Bible. Around 2000 years ago, a small group of radical Jews, the Hasmoneans, stood up to the powerful Greeks who ruled the world. This brave stand was all about religious freedom. Due to the miraculous nature of the victory, the Jewish people declared a new holiday. They formed Hannukah in order to commemorate and relive the Jewish ideals of the Hasmoneans.
The second Jewish holiday that was enacted by the Rabbinic leadership is Purim. Close to 2,000 years ago, the Persian leader, Haman, threatened to annihilate the Jewish people. With God's help, and a brave Queen Esther and Mordechai, the Jews prevailed against their enemies and set up an eternal Jewish Holiday to commemorate God's deliverance.
Newer Jewish Holidays
The State of Israel gained independence in 1948. Israel miraculously rebuffed 5 enemy countries - some say 6 or 7 - and won the war.
This is not a minor issue - but one of historic proportions.
19 years later, Israel was saved from yet another attempt at annihilation. In addition, Israel liberated its holiest sites - Jerusalem, Hebron, Shechem, Shilo, and Jericho.
In order to say Thank You to God, Jews celebrate Israel Independence Day and Jerusalem Day each year.
There are other holidays, but those are the primary and most famous Jewish Holidays on the calendar.