The fast day of the 10th of the Hebrew month of Tevet, which began at sunup Sunday and ends when the stars come out, commenced in Jerusalem at 5:01 AM and concludes at 5:14 PM.
The Tenth of Tevet is one of four fast days that mourn the destruction of the Holy Temple, and it marks the day in which the Babylonians under Nebuchadnezzar began the siege of Jerusalem. The other fast days for the Temple are the 17th of Tammuz, the day on which the Romans breached the walls of Jerusalem in 70 CE; the Ninth of Av, on which both the First Temple and the Second Temple were destroyed; and the Fast of Gedaliah on the third of Tishrei, commemorating the murder of Gedalia Ben Achikam, Israel's leader after the destruction of the First Temple, an event which is seen as marking the beginning of the Exile from the Land of Israel.
The fast days are intended to prompt soul-searching and repentance. On these days, Jews are meant to be awakened to the fact that our misdeeds and those of our forefathers caused these great misfortunes, and that when we repent and mend our ways, the nation's situation will be mended and we will be redeemed.
On the fast day, the 'Anenu' request is added to the Shmoneh-Esreh prayer, (a special series of 18 supplications; the Hebrew word "shmoneh-esreh" means "18" - ed.) and special Selichot (prayers asking forgiveness) are recited. In the afternoon service, the Torah portion is “VaYachel Moshe” - a special portion for fast days.
The Tenth of Tevet was also designated by the Chief Rabbinate of Israel as the Day of General Mourning for the people murdered in the Holocaust whose day of death is not known. On this day, their relatives say the mourners' prayer, or Kaddish.