'And it was in the ninth year of his reign, in the tenth month, in the tenth (day) of the month, that Nebuchadnetzar, King of Babylon came, he and all his hosts, upon Yerushalayim, and he encamped upon it and built forts around it. And the city came under siege till the eleventh year of King Tzidkiyahu. On the ninth of the month famine was intense in the city, the people had no bread, and the city was breached.' (Second Melachim 25).
Ordinarily, one must not enter Shabbos while fasting. This particular fast is an exception. In fact, according to one opinion, if the 10th of Tevet would fall out on Shabbos, we would have to fast the whole Shabbos. This is based on the similarity of the text describing the events of the day (Ezekiel 40:1) to the very wording in the Torah describing Yom Kippur (Leviticus 23:28) from which we know that Yom Kippur is never postponed.
What is so exceptional about the 10th of Tevet? Superficially, the day that the Babylonian army led by Nebuchadnezzar laid siege to Jerusalem seems less significant than the day the walls were breached (for which we fast on the 17th of Tammuz ) or the day the Temple was set afire (for which we fast on the 9th of Av). But as we learn in addiction, it is the "first sip that got us drunk", not the last drink. In other words, once the influence of lust has "breached" the walls, it is often too late. The true calamity occurs when we let the Yetzer Hara encamp around our walls in the first place.
When we let our own personal Jerusalem's be surrounded by the influences of the gentiles by watching movies, surfing non-Jewish news outlets, Youtube, Facebook and other such media, then it's only a matter of time before the city will be breached and our own personal Beis Hamikdash destroyed r"l.
Let us strengthen our fortifications on this day of Asara B'Teves. Let us accept upon ourselves to stay away from such websites, and install a strong filter, such as K9, and reporting software such as eBlaster or webchaver.com. This way, you are not tempted to change anything on your own and can begin to feel truly FREE!
And in the merit of strengthening our personal walls, may we merit that the walls of Jerusalem and the Beis Hamikdash be speedily rebuilt in our days. Amen.