Oh, I know you’ll be disappointed to find this out, but the twelve days of Christmas have no symbolic meaning at all. They’re just days. In the Church, as in the synagogue, the day begins at sunset. Therefore, Christmas begins at sundown on 24 December, which we very appropriately call ‘Christmas Eve.’ The Christmas Season, which begins with Christmas Eve, ends on the eve of Epiphany, which is sundown on 5 January. Therefore, Christmas lasts twelve days, and the period from sundown on 24 December to sundown on 5 January is called the Twelve Days of Christmas.
However, some of the days during Christmas have meanings of their own.
26 December, St. Stephen’s Day
Stephen was the first Christian martyr. You might say he was the second person to die for the Christian faith, after Jesus, so his day comes on the second day of Christmas, unless it is a Sunday, then it moves to the next available day. The song, “Old King Wenceslas” is really a St. Stephen’s Day carol, because the words are: “Old King Wenceslas looked down on the feast of Stephen.”
27 December, St. John the Apostle’s Day
St. John the Apostle was the beloved disciple, so his day is put near Christmas, to show his closeness to the Lord. According to tradition, he was not martyred, so his day comes right after St. Stephen’s Day, unless it is a Sunday, then it moves to the next available day.
28 December, Holy Innocents
After the wise men told Herod that a new king had been born in Bethlehem, Herod massacred the children in the hope of eliminating Jesus, whom he perceived as a threat to his throne. Because this event is related to the nativity, we commemorate the infants on 28 December, unless it is a Sunday, then it moves to the next available day.
None of these days are allowed to fall on a Sunday, so if they do, they are postponed. In the most extreme case, if 26 December is a Sunday, Stephen’s day moves to 27 December, John’s day gets bumped to 28 December, and Holy Innocents wind up on 29 December.
1 January, Holy Name
The first of January is the eighth day of Christmas. On the eighth day of their lives, Jewish baby boys are circumcised and given their names. So if Jesus were born on December 25, this would be the day. As recently as the eighteenth century, New Year’s Day fell toward the end of March, so the main significance of 1 January throughout Christian history has been the circumcision and naming of the Lord.
You can read more information about the church year.