It has been a family tradition to open presents on Christmas Eve, and then open our Santa presents on Christmas day.
Kate said she felt like this was definitely a European tradition that hailed from her mothers side of the family (the Swiss side). She said her mother also practiced the same tradition while she was growing up.
There seem to be many, many varieties of celebrating Christmas and handling the unwrapping of presents. The reason for moving the present wrapping could be two fold. Some families may like to concentrate more on the religious aspect of Christmas during the day, so they more the more consumer oriented portion to the night before. It could also be a way to spread out the festivities.
Many of European wedding traditions mentioned in Alan Dundes International Folkoristics book had special rituals and celebrations on Christmas Eve.
For further reference in text, see:
Etzioni, Amitai. We Are What We Celebrate : Understanding Holidays and Rituals. New York: New York University Press, 2004. Pg. 135.