Today, Sunday, December 8th, is the fast of the 10th of Tevet, one of the four days on which the Jewish people refrain from partaking of food in order to mourn the destruction of the Holy Temple.
The siege of Jerusalem began on this day, marking the beginning of the events that led to the destruction of the First Temple, the exile of the People of Israel from their land and soon after, the last vestiges of self rule for those who remained. The story is recounted at the end of the Book of Kings, Chap. 25:
"So in the ninth year of Zedekiah’s reign, on the tenth day of the tenth month, Nebuchadnezzar king of Babylon marched against Jerusalem with his whole army. He encamped outside the city and built siege works all around it. The city was kept under siege until the eleventh year of King Zedekiah. By the ninth day of the fourth month the famine in the city had become so severe that there was no food for the people to eat. Then the city wall was broken through... They killed the sons of Zedekiah before his eyes. Then they put out his eyes, bound him with bronze shackles and took him to Babylon. On the seventh day of the fifth month, in the nineteenth year of Nebuchadnezzar king of Babylon, Nebuzaradan commander of the imperial guard, an official of the king of Babylon...set fire to the Temple of the Lord...carried into exile the people who remained in the city, along with the rest of the populace and those who had deserted to the king of Babylon. But the commander left behind some of the poorest people of the land to work the vineyards and fields."
In addition to the 10th of Tevet, the three other fast days are the 17th of Tammuz, the day the Jerusalem city walls were breached, the 9th of Av, when the Temple was burned, and the 3rd of Tishrei, when the Jewish governor of those who were left in the Holy Land, was murdered.
Except for the 9th of Av which lasts from sunset to sunset, the three fasts begin at dawn and extend until nighttime. In Jerusalem, the fast begins at 5:05 a.m. and ends at 5:14 p.m. (for exact times in your location, check your local synagogue or rabbi). The fast is considered a "light" one and aside from refraining from food and drink, there are no specific prohibitions. Pregnant and nursing women do not have to fast, and work, bathing and the wearing of leather shoes, prohibited on other fasts, are allowed.
However, all four fasts are days meant for soul-searching and repentance, as well as prayers for the Redemption. Prayers designated for fasts and a special Torah reading are added to the service.
The Israeli Chief Rabbinate designated the fast of the10th of Tevet as the "Day of Kaddish," Yom Hakaddish Haklali, for those murdered in the Holocaust whose exact day of death is unknown. Relatives may recite the kaddish prayer for them on this day and it is customary for the synagogue service to include the "El Malei Rachamim" prayer, said at funerals, on yahrzeits and on the days when Yizkor is said, in memory of all the victims.