Hanukkah gelt (Yiddish for “money”) is often distributed to children to add to the holiday excitement. The amount is usually in small coins, although grandparents or relatives may give larger sums. In Israel, Hanukkah gelt is known as dmei Hanukkah.
The tradition of giving Chanukah gelt dates back to a long-standing East European custom of children presenting their teachers with a small sum of money at this time of year as a token of gratitude. The connection may be etymological: In Hebrew, the words “Hanukkah” (dedication) and “hinnukh” (education) come from the same root. In time, money was also given to children to keep for themselves.
According to Magen Avraham, poor yeshiva students would receive a gift of money from their Jewish benefactors on Hanukkah.
In the 1920s, American chocolatiers picked up on the gift/coin concept by creating chocolate gelt. Wikipedia