They are to observe these as days of feasting and gladness, and for sending delicacies to one another, and giving gifts to the poor. (Esther 9:22)
There is a beautiful custom before reading the Megillah in the synagogue, to contribute three half-dollar coins (or their equivalent) to charity. This symbolizes the half-shekel which every Jew used to give as dues to the Temple in Jerusalem (see Exodus 30:11-16).
But why does the Torah specify a half-shekel instead of a whole?
The answer is that by giving only a half, each Jew realizes that he'll never become "complete" unless he is part of the larger community. Accordingly, Jewish law states that everyone -- rich or poor -- is to give no more and no less than a half-shekel. This teaches that every Jew is equally important to our national mission. Just as removing one letter invalidates a Torah Scroll, so too the loss of one Jew hinders our destiny.
Sometimes it is through our enemies that we come to realize: Every Jew is precious and integral to the future of our nation. The Talmud says that the biggest problem of the Jewish people at the time of Mordechai and Esther was a lack of unity. It was the wicked Haman who reminded us that we stand together as one people: In plotting genocide, he referred to the Jews as Am Echad -- and planned that they should literally "hang together." In modern times as well, we've seen that the anti-Semite doesn't distinguish between an assimilated Jew and a Chassidic Jew.
ALL FOR ONE
On Purim, we send two types of ready-to-eat food to at least one friend, symbolizing the spirit of kinship which can help prevent the appearance of future Hamans. On Purim, we also give charity to at least two poor people. We reach out to each other, so that no one should miss the joy of the occasion.
It is particularly meritorious to send a gift to someone you need to make up with. Just as we would never consider distancing ourselves from a good friend based on our disagreements, so too we should never consider distancing ourselves from any Jew (or group of Jews) based on our differences. In fact, the Talmud says that the epitome of evil in this world -- Amalek, from whom Haman descends -- was born out of a Jewish refusal to accept others lovingly.
The Talmud says Kol Yisrael Araivim -- each Jew is responsible one for the other. If the boat is sinking, we're all going down. But when there is love and unity amongst us, even the wrongdoers become righteous and our enemies cannot harm us! For this reason, on Purim we give charity to anyone who asks, without investigating the validity of their need. (In contrast to the rest of the year, when we are obligated to ensure that our Tzedakah money is being disbursed properly.) On Purim, every Jew is worthy without question.
God treats us as we treat others. On Purim, if we give others the "benefit of the doubt" and don't check their worthiness, then God doesn't "check us for worthiness" either. Purim, therefore, is an auspicious time to ask God to bestow gifts of health, unity and a speedy redemption for the Jewish people.
HALACHAS (LAWS) OF GIVING GIFTS ON PURIM
1) Mishloach Manot is fulfilled by sending two types of ready-to-eat food to at least one friend. This mitzvah should be performed on Purim day itself.
2) There is a custom to send Mishloach Manot through a third person messenger, since the word Mishloach is related to the word for messenger, Shaliach.
3) Matanot La'evyonim is fulfilled by giving money to at least two poor people on the day of Purim. The gift should at least equal the value of a fast-food meal.
4) This is not a "family" obligation, but rather each person should perform the mitzvah themselves.
5) The money needn't be given directly to a poor person, but can be given to a community representative -- as long as the money is actually distributed to the poor on Purim day.
6) Matanot La'evyonim is a special mitzvah, not to be included in the amount of money a person sets aside for charity during the rest of the year.
7) Maimonides writes that it is inappropriate to buy expensive Mishloach Manot, if this will come at the expense of larger gifts to the poor.