“And it happened in the ninth year of [Zedekiah’s] reign, in the tenth month [i.e., Tevet], on the tenth of the month, that Nebuchadnezzar king of Babylon came - he and all his army - against Jerusalem, besieged it and built a siege tower around it.” (II Kings 25:1, Jeremiah 52:4)
Zedekiah was the very last king of Judah, who had ascended the throne in a turbulent period of Jewish history. 
Zedekiah was the very last king of Judah.
One hundred and twenty-two years earlier, Shalmaneser, king of Assyria, had conquered the northern kingdom of Israel; he took King Hoshea captive and sent the ten tribes into exile, scattered throughout the Assyrian Empire, where they were lost to the Jewish national body. The southern kingdom of Judea would survive for another 133 years, under constant threat of invasion and occasional incursions from Egypt and Babylon, before finally being invaded and conquered by Nebuchadnezzar.
Zedekiah’s father, Josiah, had reigned for thirty-one years. He had ascended the throne when he was just eight years old, and tried desperately to repair the spiritual ravages that his predecessors had caused to the nation: he renovated the Holy Temple in Jerusalem, which had not been maintained properly since King Jehoash, eight kings and over 200 years previously; he restored the Torah to Judah; he destroyed the idols, including the Asherah tree from the Holy Temple, and burned them all; he dismissed the priests of idolatry and destroyed the rooms that they had maintained within the Holy Temple; he destroyed all the idolatrous altars throughout the Land; and he restored the Pesach sacrifice, which had been neglected for centuries.
His reign came to an abrupt end when Pharaoh Neco wanted to traverse through Judea on his way to fight Assyria. King Josiah would not tolerate a foreign army on Judean soil, so he confronted the pharaoh in Megiddo. In the ensuing battle, Pharaoh Neco killed King Josiah, whereupon the masses anointed Josiah's son Jehoahaz as king.
Jehoahaz, however, was an evil king; and after reigning for just three months, the pharaoh captured him, exiled him, reduced Judea to a vassal state, and put Jehoaz's brother Eliakim on the throne, changing his name to Jehoiakim. Jehoiakim, also an evil king, reigned for eleven years, first as a vassal of Egypt, then of Babylon. Eventually, a Babylonian-Moabite-Ammonite alliance attacked Judea, inflicting terrible damage. Jehoiakim died, and his eighteen-year-old son Jehoiachin became king. Jehoiachin was just as evil as his father and, after he reigned for just three months, Babylon besieged Jerusalem, pillaged the treasures of the Holy Temple, exiled tens of thousands of Jews, and took King Jehoiachin into captivity in Babylon.
The king of Babylon then crowned Jehoiachin’s uncle, Mattaniah, as vassal-king of Judea, changing his name to Zedekiah. And then, after nine years of autonomy in the Babylonian Empire, on the tenth of Tevet, the Babylonian army began its siege on Jerusalem, the last stage before the final obliteration of Jewish independence. Just seven months later, on the 7th of Av, Nebuzaradan, the chief executioner of Babylon, would arrive in Jerusalem to burn the Holy Temple two days later - on the 9th of Av.
The 9th of Av had been ordained as a day of destruction and mourning ever since the spies whom Moshe had sent to spy out the Land of Israel had returned, given their evil report, and the nation spurned the Land of Israel and cried in their lack of faith. The Talmud (Ta’anit 29a) calculates the Torah’s chronology: on the 20th of Iyar we left Mount Sinai (Numbers 10:11); this was followed by a three-day journey (v.33) concluding on the 23rd of Iyar; a 30-day sojourn in Kibroth-Hata'avah (ibid. 11:20, 34) concluding on the 22nd of Sivan; and finally seven days in Hazeroth (11:35, 12:15-16) before reaching the Paran Desert (ibid. 12:16) on the 29th of Sivan.
Hence, Moshe sent out the twelve spies on the 29th of Sivan (compare Targum Yonatan to Numbers 13:20). They returned forty days later on the 8th of Av and gave their evil report of the Land; and when night fell and the nation cried, it was the evening of the 9th of Av. Instead of the 9th of Av being the day that we entered the Land of Israel and brought the redemption, it became a day of tragedy.
But what event foreshadowed the siege of Jerusalem beginning on the 10th of Tevet?
It seems to me that the Torah gives us a hint of what the background was.
It seems to me that the Torah gives us a hint of what the background was. 1,291 years before the First Temple was destroyed, three angels appeared to Abraham and Sarah, heralding the birth of their son Isaac the following year (Genesis 18:1-14). The Talmud and the midrashim are consistent about the chronology: the angel promised Sarah that she would bear her son Isaac exactly one year hence (18:10); the 400 years of Abraham’s seed living as “strangers in a land not their own” (15:13) began with the birth of Isaac and finished with the Exodus from Egypt. Since the Exodus occurred on the 15th of Nisan, Isaac was born 400 years to the day earlier; i.e., also on the 15th of Nisan. And since the angelic prophecy to Sarah was one year to the day before Isaac was born, this episode also happened on the 15th of Nisan.
This was also the day before God destroyed Sodom and Gomorrah, sparing only Lot and his two daughters, who fled into the hills (Genesis 19:1-25). The night following the destruction, Lot’s daughters, fearing that they were the only three people remaining in the world, plied their father with drink and impregnated themselves by him. They gave birth to sons - the elder bore Moab and the younger bore the ancestor of Ammon (19:30-38).
Nine months after the 16th of Nisan brings us to the 10th of Tevet. Hence, Moab and Ammon, the two nations who, in alliance with Babylon, would attack Judea and thus initiate the process that would culminate in Judea being captured and the Holy Temple destroyed, were born on the 10th of Tevet - the day that Babylon began the siege on Jerusalem.
Thus, Jewish independence would be extinguished in the Land of Israel and, for the next 70 years, the Land was to lie desolate under Babylonian occupation. At the end of that time, the Persian King Cyrus (Koresh) defeated Babylon, inherited the Babylonian Empire - including Israel - and proclaimed the right of any Jew who wanted to return to Israel and to rebuild the Holy Temple.
In the days of the Second Temple, we did not fast on the fast days of mourning (the 17th of Tammuz, the 9th of Av, Tzom Gedaliyah on the 3rd of Tishrei, and the 10th of Tevet): one does not mourn over the destruction on the Temple while the Temple is standing. The Rambam, however, states that the Jews did fast on the 9th of Av in the Second Temple period (commentary to the Mishnah, Rosh HaShanah 1:3; "Laws of Fasts" 5:5).
It seems puzzling that we should fast in mourning for the Temple when the Temple is standing. The Maggid Mishneh (commentary on the Mishneh Torah by Rabbi Vidal of Tolosa, 14th-century Spain) explains: “According to our rabbi [the Rambam], the custom [whether or not to fast] depends upon the circumstances, as the Talmud [Rosh HaShanah 18b] makes clear. In a time of peace - which means when the Holy Temple is built - the fast days are days of rejoicing and gladness; in times of persecution, they are fast days; and in times when there is
The Second Temple, being only temporary, could annul three of the four fasts of mourning.
neither peace nor persecution, every Jew who desires to fast can fast. However, fasting is not obligatory, with the exception of the fast of the 9th of Av, because there were so many disasters on this day. But now, everyone fasts on all these days and all are obligatory upon every Jew until the Holy Temple will be rebuilt.” (Maggid Mishneh on "Laws of Fasts" 5:5)
Evidently, the Second Temple, being only temporary, could annul three of the four fasts of mourning. But the 9th of Av is such a disastrous day that a temporary Temple cannot override it.
But the third and final Holy Temple will convert even the 9th of Av into the day of joy and festivity that it was originally intended to be, a day of redemption: “Thus said HaShem, Lord of Legions: The fast of the fourth [month, i.e., Tammuz] and the fast of the fifth [month, i.e., Av] and the fast of the seventh [month, i.e., Tishrei], and the fast of the tenth [month, i.e., Tevet] will turn into rejoicing and gladness and festivities for the House of Judah. So love truth and peace.” (Zechariah 8:19)