The tenth day of the Hebrew month of Tevet (this year, January 1), is one of the more obscure and poorly understood dates on the Jewish calendar. The best-known explanation is that it commemorates the beginning of the siege of Jerusalem by the Babylonians, eventually leading to the destruction of the First Temple in 586 B.C.E. and the dissolution of the Judean kingdom. Jeffrey Woolf analyzes the significance of the event in light of the biblical prophets:
[The prophet Ezekiel] knew what was going to happen, for he himself had a vision of the catastrophe for which the people were headed. But when the day [of the Babylonian attack on Jerusalem] actually arrived, he found it difficult to assimilate what was happening and therefore the Holy One, blessed be He, had to tell him emphatically, time and again, that this was indeed the reality. Little wonder, therefore, that the rest of the people were even more deeply traumatized when Jerusalem was put under siege. The stern lesson of the tenth of Tevet—that Jerusalem was vulnerable on account of the nation’s corruption—was what led the people to include the day on which the siege of Jerusalem began among the days of mourning and commemoration for the destruction of the First (and later also the Second) Temple.
Read more on YU Torah: http://www.yutorah.org/lectures/lecture.cfm/753854/Rabbi_Dr_Jeffrey_Woolf/Why_the_Tenth_of_Tevet