The Hebrew word Chanukah shares the same root as chinuch, education. The occupying Greek forces were determined to force Hellenism upon the Jewish population, at the expense of the ideals and commandments of the holy Torah. Unfortunately, they were quite successful in their endeavor. After the Greeks were defeated it was necessary to re-educate the Jews—to reintroduce a large part of the population to Torah values. Thus the strong link between Chanukah and education.
Appropriately, during Chanukah it is customary to give gelt (money) to children, to teach them to increase in charity and good deeds, and to add to the festive holiday spirit.
This subtle form of “bribery” is an essential component in the educational process. Maimonides discusses the importance of using incentives and prizes until a child is old enough to independently understand the importance and beauty of the Torah and mitzvot.
There is also a deeper reason for this age-old custom:
In his record of the Chanukah events, Maimonides writes: “The Greeks laid their hands upon the possessions of Israel.”
The Greeks invaded the possessions of Israel in the same spirit in which they defiled the oil in the Holy Temple. They did not destroy the oil; they defiled it. They did not rob the Jewish people; they attempted to infuse their possessions with Greek ideals—that they be used for egotistical and impure ends, rather than for holy pursuits.
Chanukah gelt celebrates the freedom and mandate to channel material wealth toward spiritual ends.
Chanukah gelt can be given any time throughout Chanukah (aside for Shabbat). Some have the admirable custom of gelt-giving each weeknight of Chanukah. In Chabad, it is customary to give gelt every night, but to hand out a heftier sum on the fourth or fifth night.