The Babylonian armies of King Nebuchadnezzar breached the walls of Jerusalem on the 9th of Tammuz in the year 3338 from creation (423 BCE); King Ziddikiahu of Judah was captured and taken to Babylon (Jeremiah 39:5. A month later, the capture of Jerusalem was completed with the destruction of the Holy Temple and the exile of all but a small number of Jews to Babylon). Tammuz 9 was observed as a fast day until the second breaching of Jerusalem's walls (by the Romans) on the 17th of Tammuz, 3829 (69 CE), at which time the fast was moved to that date. (Talmud, Rosh Hashanah and Tur Orach Chaim 549)

Links:
thethreeweeks.com
The Destruction