I think Epiphany is about celebrating the day when the three Magi came to Bethlehem and found Jesus there. Basically, December 25 is about celebrating the birth of Jesus according to the Gospel of Luke, and Epiphany on January 6 would be about celebrating the arrival of the Magi according to the Gospel of Matthew. Or so I think. Correct me if I'm wrong.
As for why we celebrate Boxing Day in Sweden (and in several other parts of Europe), I don't think there is an obvious religious reason for it. However, the Vikings celebrated their winter holiday, the yule, before they were Christianized. So here in Scandinavia, the midwinter festivities are older than the celebration of the birth of Christ. The yuletide holidays lasted longer than just one day, and it could be that the Vikings couldn't accept the idea that they would have to exchange their long heathen holiday for a single day of Christmas. Maybe people simply demanded the right to keep on celebrating for at least one day more? Maybe that's one reason why we observe Boxing Day in Sweden, and in other parts of Europe as well?
Ann