On this daf, we find a baraisa that says that everyone is obligated to read the Megillah. We learn that “everyone” comes to include women, who were also part of the miracles that led to Purim.
The Rashbam in Arvei Pesochim brings from the Ri Halevi that the miracles of Purim, Chanukah and Pesach happened primarily due to women: Purim through Esther, Pesach since we find that the redemption was in the merit of righteous women, and Chanukah due to the bravery of Yehudis.
Tosafos and Hagahos Mordechai argue. Although no one argues that Purim and Pesach were primarily due to the actions of righteous women, and Chanukah was at least partially in their merit, the implication of the Gemara that “they, too, were part of the miracle” implies something different. This is clear from the Yerushalmi, which says that they, too, were in the miracle, since Paroh wished to destroy and eradicate Jewish women too. Paroh’s decree was against male babies, but the Jewish people could not have survived without Jewish men, so Jewish women would have become just as extinct, chas veshalom.
The obvious question here is why Jewish women are not obligated to sit in a sukkah on Sukkos, since they were part of that miracle too.
Tosafos and Hagahos Mordechai conclude that this rationale only applies in rabbinic decrees, not Torah obligations. Chanukah, Purim and the four cups on Pesach are all rabbinic in nature, so women are obligated in them, since they were part of those miracles.
The Bnei Yissochor adds a deeper dimension to this: “Women were involved in these miracles, since there are two aspects of endemic sin that need to be fixed before we merit a miracle. We need to rectify the sin of Adam and the sin of Chava. Since only a woman can repair Chava’s sin, without Jewish women we could not have merited any of these redemptions. The men fixed the sin of Adam and the women repaired Chava’s blemish…”
(Rashbam and Tosafos, Pesachim 118; Hagahos Mordechai ad loc.; Bnei Yissoschor).