א וּבִשְׁנֵים עָשָׂר חֹדֶשׁ הוּא–חֹדֶשׁ אֲדָר בִּשְׁלוֹשָׁה עָשָׂר יוֹם בּוֹ אֲשֶׁר הִגִּיעַ דְּבַר–הַמֶּלֶךְ וְדָתוֹ לְהֵעָשׂוֹת בַּיּוֹם אֲשֶׁר שִׂבְּרוּ אֹיְבֵי הַיְּהוּדִים לִשְׁלוֹט בָּהֶם וְנַהֲפוֹךְ הוּא אֲשֶׁר יִשְׁלְטוּ הַיְּהוּדִים הֵמָּה בְּשׂנְאֵיהֶם
1. And in the twelfth month – which is the month of Adar – on the thirteenth day of it, the word and law of the king were revealed to perform on that day that which was planned by the enemies of the Yehudim to conquer them. And it was turned around that the Yehudim conquered their haters.
According to Midrash Shmuel, the verse stresses that this occurred on the 13th of Adar because it was a miracle that so much time time passed since Sivan, and Achashverosh still hadn’t changed his mind despite the fact that the Talmud (Megillah 15b) describes him as fickle. He often changed his opinion on various important issues, including his feelings for his wife.
According to the Ben Ish Chai, the significance of the 13th because it shares the same gematria as echad (1+8+4=13) (“one”). Only H-Shem is One (Devarim 6:4), and the verse then teaches that H-Shem always saves His people.