Sh'mini Atzeret
Sh'mini Atzeret is the only festival that appears in the Torah without an explanatio for its observance. It is very similar to, and a part of, the Sukkot holiday, although the four species are no longer used on Sh'mini Atzeret. Congregations read the book of Ecclesiastes, make prayers of thanks for rain, and finish with a Yizkor (memorial) service.
Chanukah commemorates the historical and spiritual victory of Judah Maccabee and his sons over the Syrians who has attacked and defiled the Holy Temple in Jerusalem. There is a legend that the Syrains were failing in their efforts to force Jews to abandon their religion, destroyed all of the ritual and Holy objects in the synagogue, hoping to end their worship this way. A tiny amout of oil was found in the ruins, and men were sent to fetch more so that the eternal light should continue to burn. It was an eight-day journey and there was only enough oil for the light to burn for a single day. Miraculously, the oil lasted the entire eight days until more was brought. This is the miracle of the light over darkness the Chanukah celebrates.
Tu B'Shevat means "the fifteenth of Shevat" (the name of a month in the Hebrew calenday). It is celebrated as the "New Year for the Trees," because it marks the time of the earliest blooming trees after the winter in Israel.
Purim is a spring holiday, and it commemorates the salvation of the Jewish people from obliteration by an evil politician named Haman. Queen Esther fasted along with her uncle Mordecai and all of the Jewish people when they faced this ordeal. Each year the Torah Scroll of Esther is read in Synagogue in memory of Esther and Mordecai.