Where did Christmas originate?
Christmas is celebrated on December 25th, which is very close to the winter solstice. Many pagan cultures had festivals (even regarding the sun) around the time of the winter solstice e.g. the Viking celebration of Yule in late December. Early Christians simply used these established, and well-loved, festivals to celebrate the birth of THE Son, Christ.
In the first couple of centuries of the Christian church, Christianity existed alongside pagan religions including that of Rome, although most Christianity was practiced in secret for fear of persecution.
According to an old Judaeo-Christian tradition, March 25th was supposed to have been the date for 'Creation'. The early Christian writer Sextus Julius Africanus (220 A.D.) thought this dating quite possible and suggested that Christ therefore became incarnate on that date. According to Julius, since Jesus became incarnate from the moment of his conception, this meant that, after nine months in Mary's womb, Jesus would have to be born on December 25th.
It wasn't until the 18th century that other possibilities were put forward. These included having Christmas on December 25th to coincide with the winter solstice or the festival of Saturnalia. However, as the solstice is on 21st December and Saturnalia usually began on the 17th and lasted no more than a few days, so neither of these dates seem to coincide with 25th December.
Nevertheless, when Christianity became the official religion of the Roman Empire in the fourth century, the Christian festival of Christmas totally replaced the festival of Saturnalia and the pagan rites surrounding the sun-worship and the solstice. For the same reasons ancient churches were often built on old pagan sites of worship so that it could be seen that Christianity had categorically replaced the old pagan religions rather than adopting pagan customs or sitting alongside pagan religions.
Where old customs were difficult to replace, Christianity 'Christianized' these rather than ban them outright. As an example, at the solstice (and at Saturnalia) it was the custom in England to bring into the house the three most common indigenous plants that were thought of as somehow 'magical' (because they were poisonous and also by the fact that they did not shed their leaves in winter). These were holly, ivy and mistletoe. However, the Church Christianized holly (saying that its leaves represented Christ's crown of thorns and the berries his drops of blood) and the ivy plant (saying that its three-part leaves represented the Trinity). The mistletoe, however, was never given a Christian symbol, and so it is still not used in Christian Churches as a decoration to this day as it is a purely pagan symbol rather than a Christianized one.
Of course, Jesus was not really born on December 25th. We know this for certain as we are told in the Bible that the shepherds were in the fields the night he was born - not an option in winter! But nevertheless, because of the history of December 25th being accepted by Sextus Julius Africanus, we still celebrate the birth of Christ on this date to this day.