The siege was emplaced around Jerusalem for three years by the superpower of the time, Babylonia. The ensuing destruction of Jerusalem led to the exile of the Jews to Babylonia (today's Iraq). Further information on the siege can be found in the Book of Kings II, chapter 25.
The fast is the shortest of the six annual Jewish fasts, ending at 5:22 PM in Jerusalem and approximately 5:10 PM in New York.
The 10th of Tevet (Asarah B'Tevet) has also been designated by Israel's Chief Rabbinate as the day of mourning for Holocaust victims whose date of death is unknown. The day is known as the "Day of General Kaddish (mourners' prayer)."
The renowned Maimonides wrote in his Jewish Law Code, "The essential significance of the fast of the Tenth of Tevet, as well as that of the other fast days, is not primarily the grief and mourning which they evoke. Their aim is rather to awaken the hearts towards repentance; to recall to us, both the evil deeds of our fathers, and our own evil deeds, which caused anguish to befall both them and us and thereby to cause us to return towards the good."
Rabbi Avraham Danzig of Poland (1748-1820) wrote in his work Chaye Adam, "...Therefore, the people who fast but engage in pointless activities, grasp what is of secondary importance and miss what is essential. Nevertheless, repentance alone without fasting is also insufficient, because there is a positive commandment of Rabbinic origin to fast on this day."