What is Christmastide, perhaps you are wondering? In most protestant churches, we tend to ignore the "seasons" of the church that have historically been set apart as the flow of the calendar for Christians, but in some Christian churches (protestant, Eastern Orthodox, and Catholic alike) a liturgical calendar guides how the different seasons of the Christian year are distinguished. Christmastide is the brief season from Christmas Day to January 5.
Also called Yuletide or simply the Twelve Days of Christmas, Christmastide marks the season during which the church has historically reflected on the significance of the incarnation. If Advent is a season of anticipation, then Christmastide is a season of fulfillment and a beginning awareness of what that fulfillment means.
Christmastide includes consideration of the various early events of Christ's life, including visitation from the shepherds, the visitation and gifts of the Magi, and the circumcision of Jesus. It ends on what has traditionally been called Twelfth Night, which is the eve of the day of Epiphany (which is sometimes called Three Kings' Day). Just as Advent is a season that culminates with Christmas Eve, Christmastide also culminates with the eve of the next season.
I think it is very helpful to observe the seasons, rather than simply celebrating the days and having a gap of time in between. For me, all that happens in anticipation of Advent is more than I want to contemplate all at once, so I'm thankful for a season of four weeks or so to consider it. Likewise, the significance of the incarnation is more than I want to try to think through on just one day (Christmas Day), so I appreciate having a season for reflection on that.