I was raised in a Jewish but non-observant family in a small town in upstate New York. As a minority in this community, I was jealous of the gifts my Christian friends received for Christmas. In response, my parents gave us gifts to celebrate Hanukkah. I always understood this to be a commemoration of the rebuilding of the Temple in Jerusalem when the Jews defeated the Maccabees around 200 B.C.E., and they found the oil to light the Temple lasted for eight days instead of one –thus having to light candles on the menorah for the eight nights of Hanukkah.
As it turns out there are many origins of the Hanukkah story and especially the tradition of gift giving. One possibility is the defeat of the Maccabees as I recalled; the others are matching gift giving at Christmas; and one more is the Greeks giving gifts to celebrate victories. In truth, the habit of gift giving with lighting of the candles is more of a modern tradition.