"Chanukah gelt" is a Jewish custom rooted in the Talmud.
The Talmud states that even a very poor person must light Chanukah lights, even if he can't afford it. A person with no money is required to go "knocking on doors" until he collects enough to buy at least one candle for each night of Chanukah.
The Torah concept of charity - tzeddakah - requires us to help the recipient in the most dignified manner possible. Therefore, the custom arose to give gifts of money during Chanukah so that someone who needs extra money for Chanukah candles can receive it in the form of "Chanukah gelt."
