On the 10th of Tevet of the year 3336 from Creation (425 BCE), the armies of the Babylonian emperor Nebuchadnezzar laid siege to Jerusalem. Thirty months later -- on Tammuz 17, 3338 -- the city walls were breached, and on 9 Av of that year, the Holy Temple was destroyed. The Jewish people were exiled to Babylonia for 70 years.
Link: Asarah B'Tevet
Tevet 10 is observed as a day of fasting, mourning and repentance, in remembrance of the siege of Jerusalem. We refrain from food and drink from daybreak to nightfall, and add the Selichot and other special supplements to our prayers. (More recently, Tevet 10 was chosen to also serve as a "general kaddish day" for the victims of the Holocaust, many of whose day of martyrdom is unknown.)
Links:
Learn about Tevet 10
Essays and Stories on the Holocaust
When you come to a place that seems outside of G‑d’s realm, too coarse for light to enter, and you want to run away—
—know that there is no place outside of G‑d, not even this place, and rejoice in your task of uncovering Him there.