The source for Mishloach Manot is found in the book of Esther in chapter 9. Immediately after the military victory over their enemies the Jews celebrated and established a day of festivities and joy, called Purim. The way they celebrated this holiday was by having a big feast, the giving of "Mishloach Manot Ish L'Re'ehu" (gifts of food to one's friends) and giving money to the poor (9:19,22).
Why is it that sending Mishloach Manot was chosen as one of the ways to celebrate this special day? What is so significant about sending food to one's friends? Why does it have to be food?
The first classic approach to this question has its roots in the early commentaries who write that Mishloach Manot is part of the Mitzvah (commandment) of the Se'udah (festival meal) [see Rambam Megillah 2:15, Shibolei HaLecket 201, Tur 695, Shulchan Aruch 695:4].
It is for this reason that the food one gives as Mishloach Manot must be a food item. Moreover, it is for this reason these food items must be able and ready to be eaten right away at the Purim meal. Furthermore, not only must it be edible for the meal, it must also be in accordance with what the person normally eats. The Ran (7a) rules that for a rich person one must give him/her 'rich-man's food,' and if not one does not fulfill the Mitzvah; while for a poor person, since a poor person is not used to rich food, one only needs to give him the type of food he is used to fulfill the Mitzvah..
The Terumat HaDeshen (1:111) takes this a step further. He explains that there is no intrinsic significance in Mishloach Manot other than its connection to the meal. For he feels that the reason one must give Mishloach Manot is because having a big festive meal on Purim is so important that we want to ensure that every single person has a festive meal, including poor people. Therefore, to ensure that everyone has a meal, we give gifts of food to everyone, so no poor person is too embarrassed to accept food from anyone. In fact, there are those commentaries who attach the Mitzvah of Mishloach Manot to the Mitzvah of Matanot Le'evyonim (monetary gifts to the poor) because of their common theme (Semag, Ohr Zaruah 1:372, Rokeiach 237:9, Kol Bo).
The second classical approach to Mishloach Manot is found most explicitly in the 16th century Kabbalist R. Shlomo Alkabetz (author of Lecha Dodi - found in his Sefer Manot Levi p. 208, see also Teshuvot Chatam Sofer 1:196) who explains that Mishloach Manot is an expression of joy and friendship - two important themes of Purim.
This approach has much support from the Book of Esther. The Pesukim themselves establish Purim as a holiday of "Yom Mishteh V'Simcha. . .ish L'Re'ehu," "a day of feast and happiness.. man to his friend" (Megilat Esther 9:19,22). Moreover, we learn from the book of Nechemiah, upon Ezra and Nechemia's success in getting the people of Israel to do sincere repentance, they announce to the people: "today is holy for G-d, do not mourn or cry... go eat fatty foods, drink sweet drinks, and send Manot to your friends." We see from here that in Biblical times, sending food to another was a common expression of friendship and joy (See also the Bach 695:4).
An interesting practical ramification of this understanding is found in the writings of R. Sternbach (Sefer Mo'adim U'zemanim). He takes this aspect of joy and friendship so far that he rules that if one gives Mishloach Manot and the receiver does not know who the giver is (such as if one left the Mishloach Manot at the door without one's name written on it, or if the name tag happened to fall off, or if one gave it to a child who does not remember who the giver was), the giver does not fulfill his obligation. The reason is because: the receiver does not know who sent it, thus the goal of spreading friendship has not been accomplished.
A third approach, is suggested by R. Avraham Gurwicz in his Ohr Avraham (p. 92). He combines the above two approaches, connecting the fundamental theme of Simcha to the Se'udah. He writes that to have and spread Simcha and friendship in the most optimum form, one should invite all of one's friends and relatives to a meal/party. The only problem is that if this was so, then only one person would be able to properly fulfill the Mitzvah, because there can be only one host to a party! And for each family to have a separate party with no guests is no party either! Therefore he suggests that it is for this reason that we give Mishloach Manot. This way each person symbolically shares his meal/party with another by giving them a portion of food that they will use in their meal/party.