The thirteenth of adar, ta'anit Esther, is observed as a fast day in commemoration of the fast observed by Mordechai, Esther, and all Israel. On the thirteenth of Adar, the enemies of the Jews had planned to subjugate and destroy them, but the opposite occurred, and the Jews held dominion over their enemies."The Jews gathered in their cities..." (Esther 9:1-2).
Whenever they were faced with war, the People of Israel fasted. Thus we find that Moshe fasted before he entered into battle with Amalek. The reason for such fasts is to affirm that man does not prevail because of his physical strength or prowess, but only when he lifts his eyes in prayer to Heaven so that he might be granted Divine mercy to prevail in battle.
This then was the purpose of the fast observed by Israel at the time of Haman, as they gathered to defend themselves from those who sought to destroy them. And in memory of that fast, an annual fast was established for generations on the same day. Through this we recall that G‑d accepts each person's prayer and penitence at the time of trouble.
The acceptance of this fast on the thirteenth of Adar is alluded to in the Megillah, for the verse states: "As they had accepted upon themselves and upon their descendants, these forms of fasting and supplication (ibid. 9:31)."
The fast is referred to as the Fast of Esther, for it was she who had first requested that the people fast, as she said to Mordechai: Go and gather all the Jews who are in Shushan and fast on my behalf. Do not drink and do not eat for three days, neither by night nor by day. My maidens and I will also fast in this manner (ibid. 4:16).
Our fast is not observed for three days as was the case with this original fast. Moreover, Esther's original fast was on the thirteenth, fourteenth, and fifteenth of Nissan for that was when Mordechai learned about Haman's intentions and about the royal letter written on the thirteenth of Nisan which called for the destruction of the Jews.
Our fast is observed on the thirteenth of Adar, to commemorate the fast of the Jews who had gathered to defend themselves. Because Esther had proposed the first fast to deal with the pending calamity, all of the subsequent fasts decreed during that period are referred to by her name.
Some maintain that our fast on the thirteenth of Adar does indeed commemorate Esther's three-day fast. However, since the annual fast could not be held in Nissan, for fasting is prohibited in that month, the Sages designated that it be held on the thirteenth of Adar which had been decreed a day of fasting when the Jews gathered to defend themselves.
Although Esther's fast was three days long, the Sages were lenient and decreed that the commemorative fast last only one day.