The Talmud (Megillah 5b) explains each of the different expressions for this holiday to mean a different method for celebrating the day. Simcha (“joy”) is interpreted as not giving eulogies (in the event of a death); v’mishteh (“and feasting”) is interpreted as prohibiting fasting; and v’yom tov (“and the holiday”) is interpreted as prohibiting work on Purim. Later, the Talmud (Megillah 7a) interprets the phrase mishloach manos (“sending gifts”) as the requirement to send through a messenger at least two kinds of food to at least one friend.
The Rambam (Mishneh Torah, Hilchos Megillah 2:15) writes that even two poor people are required to send another poor person some food to fulfill their obligations.
The Trumas HaDeshen writes that the exchange of food is intended to make sure everyone has enough for the feast.
M’nos HaLevi writes that we send gifts to promote friendship because achdus (“unity”) rescued the Jews.
The Midrash HaGadol on Devarim points out that this demonstrates the greatness of chesed because we were rescued because of it.
Ginzei HaMelech writes that we use a messenger because this shows achdus (“unity”) in requiring another person to get involved in this mitzva. Similarly, he points out, this is why Megillas Esther always uses Yehudim for Jews, since the root of that word is echad, one. Furthermore, the giving of gifts through messengers acts as an additional tikkun for Yaakov’s giving gifts (Bireishis 32:14-17) to Eisav, the ancestor of Amalek, through messengers.
The Vilna Gaon and Midrash Shmuel note that the Jews’ celebrating in this way parallels the three parts of Haman’s plan (Esther 3:13); the joy serves to counteract Haman’s plan to destroy the Jews, the feasting serves to counteract Haman’s plan to kill the Jews, and the Yom Tov serves to counteract Haman’s plan to annihilate the Jews.
The Vilna Gaon writes that, eventually, Purim was not accepted as a full Yom Tov because that would keep people from performing the other mitzvos of Purim.
Rav Gallico stresses that the verse mentions the Yehudim celebrating to point out that they did so despite their necessary exhaustion.
With the Jews in Shushan still struggling, the Ginzei HaMelech notes, the Jews’ celebration of persumei nisa (“publicizing the miracle”) and feasting was intended to inspire the remaining Jewish warriors.
In his introduction to Yosef Lekach, Rav Eliezer Ashkenazi notes that a significant difference between Chanukah and Purim is that one is not required to celebrate Chanukah with a feast, per se. Since there were Jews still perishing in battle on Chanukah, we cannot institute a national feast. On Purim, however, the celebration requires both feasting and joy because not one single Jew died.
According to the Ben Ish Chai, we need both actions to celebrate both the spiritual renewal, and the physical safety.
The Sfas Emes emphasizes this by noting that, grammatically, the verse uses the word v’aso (“and he made”), implying that H-Shem made this into a day of joy and celebration.
R’ Yitzchak Hutner notes that any holiday from the Written Torah requires a degree of joy, as the Rambam (Mishneh Torah, Hilchos Yom Tov 6:18) makes clear. The holidays from the Oral Torah require drinking. Since this holiday contains aspects of both the Written and Oral Torahs, Purim requires both joy and feasting.