Victory and the Celebration of Purim
The day decreed for the attack on the Jews, and subsequently for the Jews to strike out against their enemies in self-defense—even preemptively if deemed necessary—finally arrives (Esther 9:1 Esther 9:1Now in the twelfth month, that is, the month Adar, on the thirteenth day of the same, when the king's commandment and his decree drew near to be put in execution, in the day that the enemies of the Jews hoped to have power over them, (though it was turned to the contrary, that the Jews had rule over them that hated them;)
American King James Version×). The 13th day of the 12th month, Adar, corresponds to March of 473 B.C. This day had been determined by Haman's superstitious casting of lots, but it seems likely that God had interfered in the process—causing the date to be sufficiently late enough for the Jews to both determine who their enemies were and to make preparations against them. On this fateful day that the enemies of the Jews had hoped to prevail, the opposite happened.
Besides the general fear that had come on the people of the empire because of the Jews' apparent divine favor and help, we are told that the officials of the land helped the Jews on this occasion because of their particular fear of Mordecai's growing influence in the empire (verses 2-4). They may have been trying to garner political favor with the new prime minister, and at the very least were trying to secure themselves against any possible reprisal.
In verses 7-14 we see a return to the conflict with Haman in the killing of his 10 sons. "The patterns of reprisal and vengeance were so deeply ingrained in the cultures of the ancient Middle East that the survival of even one of these sons might mean trouble for the next generation of Jewish people. By listing each of the vanquished sons of their mortal enemy, the Jewish people celebrated the fact that the victory was complete" (Nelson Study Bible, note on verses 7-10). It could also be that these sons had taken or threatened action against the Jews at some point. Moreover, we may perhaps see in this a continuation of the carrying out of the ancient divine edict of destroying the Amalekites. King Ahasuerus granted Esther's request that the bodies of Haman's sons be publicly displayed on the gallows (verses 11-14). This was to serve as a deterrent against anyone contemplating harm against the Jews.
Having overcome their enemies on Haman's determined day, the Jews set aside the next day, the 14th of Adar, as a holiday for celebration. The Jews at Shushan, however, were granted permission to continue fighting through the 14th. So they set aside the 15th as the day to celebrate (verses 13-19). Mordecai sent a letter directing the Jews to observe both days annually from then on and this became an accepted custom (verses 20-25, 27). The days were referred to as Purim, named after the word pur, meaning "lot" (verse 26; see verse 24; 3:7). Purim is the plural.
At some point Esther sent out a second letter with Mordecai confirming the tradition of observing Purim (Esther 9:29-32 Esther 9:29-32  Then Esther the queen, the daughter of Abihail, and Mordecai the Jew, wrote with all authority, to confirm this second letter of Purim.
 And he sent the letters to all the Jews, to the hundred twenty and seven provinces of the kingdom of Ahasuerus, with words of peace and truth,
 To confirm these days of Purim in their times appointed, according as Mordecai the Jew and Esther the queen had enjoined them, and as they had decreed for themselves and for their seed, the matters of the fastings and their cry.
 And the decree of Esther confirmed these matters of Purim; and it was written in the book.
American King James Version×). Though God had not established this feast in the law, it was appropriate for the Jews to commemorate God's intervention on their behalf in this annual celebration. Purim is similar in this respect to Hanukkah, which was instituted three centuries later to commemorate God's help and deliverance in the days of the Maccabees. Jesus Christ apparently went to Jerusalem for the observance of Hanukkah (see John 10:22-23 John 10:22-23  And it was at Jerusalem the feast of the dedication, and it was winter.  And Jesus walked in the temple in Solomon's porch.
American King James Version×). And as a Jew it is likely that He also observed Purim, especially as its institution is recorded in Scripture. Yet as Purim and Hanukkah are national celebrations not commanded in the law, it is not required that Christians observe them. Indeed, non-Jewish Christians would not be expected to, just as non-Americans are not expected to observe the American holidays of Thanksgiving and Independence Day.
What about the "fasting" in verse 31? "No date is assigned for this fast. Jews traditionally observe the 13th of Adar, Haman's propitious day (see Esther 3:7 Esther 3:7In the first month, that is, the month Nisan, in the twelfth year of king Ahasuerus, they cast Pur, that is, the lot, before Haman from day to day, and from month to month, to the twelfth month, that is, the month Adar.
American King James Version×, Esther 3:13 Esther 3:13And the letters were sent by posts into all the king's provinces, to destroy, to kill, and to cause to perish, all Jews, both young and old, little children and women, in one day, even on the thirteenth day of the twelfth month, which is the month Adar, and to take the spoil of them for a prey.
American King James Version×), as a fast ("the fast of Esther") before the celebration of Purim. These three days of victory celebration on the 13th-15th days of Adar rhetorically balance the three days of Esther's fasting prior to interceding with the king (Esther 4:16 Esther 4:16Go, gather together all the Jews that are present in Shushan, and fast you for me, and neither eat nor drink three days, night or day: I also and my maidens will fast likewise; and so will I go in to the king, which is not according to the law: and if I perish, I perish.
American King James Version×)" (NIV Study Bible, note on verse 31).
In the three verses that make up the short chapter of Esther 10, we see a final mention of Ahasuerus (Xerxes) and Mordecai. Xerxes reigned eight years beyond the events of chapter 9—dying by assassination in 465 B.C. We know nothing of what became of Esther and Mordecai. But they left an amazing legacy, having cooperated with Almighty God in His grand design to save His people.