The Rambam writes that Matanot La'ebyonim – giving charity to the poor on Purim – is the most important of all the Purim obligations. If a person has a limited budget, he should prioritize Matanot La'ebyonim and allocate more for this purpose than for the Purim feast and Mishloah Manot. The reason, the Rambam explains, is that there is no greater joy than lifting the spirits of those who struggle. This Misva brings joy to the recipient, to the donor, and also to the Shechina, as it were.
The Ba'al Ha'maor (Rav Zerahya Ha'levi, Provence, 12th century) cites the ruling of Rabbenu Efrayim (late 11th-early 12th century) that Matanot La'ebyonim must be given to the poor specifically on Purim day. In ancient times, villages were allowed under certain circumstances to read the Megilla earlier – on the 11th, 12th, or 13th of Adar. Nevertheless, Rabbenu Efrayim ruled, even when the Megilla was read earlier, the gifts to the poor needed to be given on Purim day – the 14th of Adar. This money, Rabbenu Efrayim explained, is given for the purpose of helping the needy enjoy a Purim feast. If one gives charity before Purim, the money might be spent before Purim. Therefore, while it is of course always a great Misva to assist the needy, the particular Misva of Matanot La'ebyonim – which is geared toward helping the poor properly celebrate Purim – can be fulfilled only on Purim day itself.
This position is cited as Halacha by the Shulhan Aruch as well as later Poskim. The Peri Megadim (Rav Yosef Teomim, 1727-1792) maintained that one may give Matanot La'ebyonim on the night of Purim, as by then, one can be certain that the money will be spent on food for Purim day. However, the Shulhan Aruch and later Poskim maintain that the money should be given on Purim day, and not the previous night.
It is common to fulfill this Misva by giving money to a Rabbi before Purim and appointing him as one's "agent" to distribute the funds to the needy on Purim. Many people are not likely to encounter a needy person on Purim itself, so they instead give the money to a Rabbi who knows those in need of assistance, so he can give it to them on Purim day. If one who does not live in Jerusalem gives the money to a Rabbi who will distribute the funds in Jerusalem on the 15th of Adar – when Purim is celebrated in Jerusalem – then he does not fulfill the Misva, because he must give charity on the day that he observes as Purim (the 14th of Adar).
While the preferred manner of fulfilling this obligation is by giving cash, one satisfies his requirement also by writing a check and giving it to a needy person. Since the recipient can take the check to the bank and receive cash to be used for purchasing food, this qualifies as Matanot La'ebyonim. Even if Purim falls on Sunday, when banks are closed, the recipient can sign the check and give it to the casher in a store, or to a friend or neighbor in exchange for cash. Hence, one can, if necessary, fulfill this Misva by giving a check.
One does not, however, fulfill this Misva by donating to the needy by charging his credit card. When one charges his credit card, the money is transferred only several days later, and so this does not qualify as a gift given on Purim itself. Theoretically, one can fulfill the Misva by charging his credit card several days before Purim, if he knows that the funds will be transferred on Purim day, though this is, of course, not very practical.
Summary: One is required to give Matanot La'ebyonim (gifts to the poor) on Purim day. One can fulfill his requirement by giving money before Purim to somebody – like a Rabbi – who will distribute the money to the needy on Purim day. It is preferable to fulfill this Misva with cash, but if necessary, one fulfills the requirement also with a check. One cannot fulfill this obligation by charging a credit card.