The Bible does not name the Hebrew months, but declares that the month containing the holiday of Passover, the month we refer to as Nisan, is the first month. The month preceding Nisan is Adar, and therefore, according to the Biblical manner of counting months, it is 12th and final month of the year.
There are seven leap years every 19 years in the Jewish calendar cycle, and during every leap year the month of Adar is doubled: there are two months of Adar, Adar aleph and Adar bet. In a leap year, the holiday of Purim, celebrated on the 14th of Adar, is celebrated in Adar bet.
The month of Adar contains the festive holiday of Purim which falls out on its 14th day. As such, the Talmud (Taanit 29a) instructs to increase in joy the entire month. As Adar precedes Passover, it was, in fact, the last month that the Jews spent enslaved in Egypt, making it a time of joy. We also rejoice over the salvation of the Jews from the decree of the evil Haman at the time of Purim.
This is precisely the opposite of the month of Av in which Jews decrease joy to commemorate the sad events that took place in that month, most notably the destruction of both Temples.
The central theme of the holiday of Purim is turning light into darkness, referred to as venahafoch hu, which means things turning upside down or reversing the situation in a surprising way.
And so, on the thirteenth day of the twelfth month—that is, the month of Adar—when the king’s command and decree were to be executed, the very day on which the enemies of the Yehudim had expected to get them in their power, the opposite happened, and the Yehudim got their enemies in their power. Esther 9:1
This is epitomized by Haman’s choice of when to annihilate the Jews, which he accomplished by throwing lots. By chance, the 13th of Adar came up. Haman was thrilled, as the 7th of Adar was the day that Moses died. He assumed that the month was a dark time for the Jews. What Haman didn’t know, however, was that the same 7th of Adar was also the day that Moses was born. Thus, the month that Haman thought was a time of darkness was actually a time of great joy for the Jews.
During the Second Temple period, there was a Jewish custom to make a public proclamation on the first day of the lunar month Adar, reminding the people that they are to prepare their annual monetary offering to the Temple treasury, known as the half-shekel.