The ninth month answers to our December, and the fast was probably in commemoration of the capture of Jerusalem by the Chaldaeans in the previous year.
Related Commentaries of Jeremiah 36:9
Jeremiah 36:9
9 And it came to pass in the fifth year of Jehoiakim the son of Josiah king of Judah, in the ninth month, that they proclaimed a fast before the LORD to all the people in Jerusalem, and to all the people that came from the cities of Judah unto Jerusalem.