January 6th is still widely observed as a holiday by many plain folks, who commemorate the Epiphany with rest and fasting. The Epiphany, traditionally, is the day in which the wise men brought gifts to Jesus. However, January 6th is called “Old Christmas” because in 1582 Pope Gregory XIII deleted ten days, eleven minutes, and fifteen seconds from the calendar, to realign it with the seasons of the year, thus technically moving Christmas from Dec. 25th to Jan. 6th. Most Amish business’ are closed on the day of Observance and spend time at home with family.
Source: http://amishamerica.com/amish-celebrate-old-christmas/