January 6th is known as Old Christmas, a traditional holiday celebrated by the Amish. Paul Miller from Behalt, the Amish and Mennonite Heritage Center in Berlin, Ohio, explained that they believe that it was twelve days after the birth of Christ that the three wise men brought gifts to baby Jesus. The visit from the three wise men is also known as the Epiphany; when Christ's divinity was revealed to the other nations of the Earth. They see it as a second day to recognize the birth of Christ and to celebrate.
Another reason that the Amish observe Old Christmas is because of the change from the Julian Calendar to the Gregorian Calendar in the 1700's. Christmas used to be celebrated on January 6th, but once the calendar was adjusted by the Pope, the date was changed to December 25th. The Amish wanted to stay with the traditional ways and continued to observe Christmas on Janury 6th. An explanation of this can be found at a site called http://www.christmas-time.com/cp-old.html.
All Amish businesses will be closed on this day in observance of the holiday. Mennonites, typically, don't celebrate this as a holiday. They recognize it in their religion; however, it is not a necessity to take a day off of work.
When visiting Ohio's Amish Country, consider staying at the Millersburg, Ohio Barn Inn Bed and Breakfast.