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
Why are you afraid? Why do you panic?
Eagerly and with purpose, your soul plunged downward to live in an earthly realm,
to enwrap herself in a body of flesh and blood.
What emboldened her? What drew her to squeeze her unbounded light
into the straitjacket of time and space?
It was neither fear, nor dread, nor panic.
It was the knowledge that here below is found beauty the highest of angels cannot touch.
Care for yourself, for your family, for your fellow human beings and our lovely planet earth, not out of fear, not from distress—
—but out of love and awe for the beauty found within all these things, the magnificence we came to this world to uncover.