Yes, it is the 10th of Tevet, a minor fast day from sunrise to sunset, and it is a mourning of the beseiging of the walls of Jerusalem by Nebuchadnezzar (prior to the destruction of the first temple, this led to the conquest of Jerusalem and destruction of the first temple) ...
I'm not sure if there was anything else bad that also happened on this day in history, but I think it is one of 4 fastdays instituted by the prophets. Or instituted by the chachamim and predicted by the prophets... Something like this...