The Feast of the Nativity commemorates the birth of the God-man, God incarnate, the Son of God, the Son of Man, the Son of David, the son of the Virgin Mary, the Rod from Jesse’s Stem, the Christ, the Messiah, God-with-us—well, to make a long story short, Jesus. (Everybody sing: “Wonderful! Counselor! The mighty God!”)
The familiar story of Christ’s birth (minus the Little Drummer Boy, who somehow got left out of the earliest accounts) (perhaps due to the fact that he was invented some 2000 years later) is given in disjoint narratives in the first chapter of Matthew and the second chapter of Luke. Speaking of making a long story short, a breathless synopsis of Luke’s account follows: Pursuant to Caesar Augustus’ taxing decree, Joseph and his pregnant (yet virginal) betrothed, Mary, traveled from Nazareth to Bethlehem, where Mary gave birth to Jesus, swaddled him, and stuck him in a feeding trough due to the “no posada” sign on the inn, while in nearby fields, angels sang bits of Handel’s Messiah to shepherds, who went into town, checked it out, and returned to their sheep oddly changed.
The New Testament does not indicate a date or even time of year for this blessed event. Some conjecture that it must have been lambing time, i.e. spring, because shepherds were abiding in the fields. (Myself, I can’t abide spring—allergies.) Hints and guesstimates about the date began to appear around the turn of the third century. Julius Africanus and Hippolytus separately calculated the day to be December 25, based on the bizarre—um, interesting—idea (attested to by Tertullian) that Jesus died on the date he was conceived, which (for Hippolytus) was the anniversary of the creation of the world (or perhaps the sun), which as it turns out was on Wednesday, March 25. Counting forward nine months then gives you December 25. I am loath to say these guys had too much time on their hands, but wow.
Other dates for Christmas were calculated by different people using different abaci. In particular, January 6 (based on pegging Easter/Christ’s conception to April 6) stuck in the Christian East for a long time, where it commemorated not only the Messiah’s birth, but also the visit of the Magi, and his baptism. When John Chrysostom decreed Christmas should be celebrated on December 25, most of the East continued to celebrate the baptism on January 6, which they (we) call Theophany. In the West, the sixth still commemorates the visit of the Magi and is called Epiphany. Nowadays only the Armenians still celebrate the Nativity on the sixth. (Old-calendar Orthodox appear to celebrate the Nativity on January 7, but that’s really December 25 on the Julian calendar.) (Confused yet?)
The idea that Christmas was dated on December 25 in order to co-opt the Roman celebration of Sol Invictus (“the invincible sun”) first showed up in an anonymous twelfth-century footnote, and was (somewhat) popularized in the eighteenth century by an anti-holiday German with Ach!s to grind. There is no evidence that Sol Invictus was celebrated before 274, making it very likely that the date was chosen to co-opt Christmas, instead of the other way around. (Oh, how it makes obnoxious Christmas-bashers mad to be told that! I trust you will use this knowledge responsibly.) It is certainly true that the modern celebration of Christmas has incorporated elements from pagan and secular sources, such as decorating trees (Germany), carols (France), and chocolate (Azteccia).
Christmas as both a religious and secular feast was outlawed in Great Britain and its colonies in the mid-seventeenth century, when the Puritans under Oliver Cromwell murdered King Charles I and took over the country. One thing you can definitely say about the Puritans is that they sure knew how not to have a good time. Christmas never really recovered from this until Dickens’ A Christmas Carol. His emphasis on Christmas as a time to be with family, coupled with a Victorian revival of the caroling tradition, brought Christmas roaring back, and it’s been roaring ever since. (Interestingly the first complaint in text of the over-commercialization of Christmas comes from 1850!) The greeting “Happy Holidays” also originated with the Victorians, but then, these were the same people who put trousers on their piano legs out of some kind of overdeveloped sense of decency.
In the Catholic Church, Christmas is a holy day of obligation, and in the Orthodox Church it is one of the Twelve Great Feasts. It is a legal holiday in many countries, and is even celebrated, at least in a secular sort of way, in many countries where Christians make up a small minority of the population. It is also the busiest day of the year for many Chinese restaurants in the United States, as many other restaurants are closed, and Jews and Atheists go to eat delicious food cooked by Buddhists, God love ’em.