There was a new religion gaining ranks in the Roman world: Christianity. This mystery cult had the Romans up at arms. Mystery in a sense that its operation was only available to iniates. Christianity in as much as participation in it's religious life is open only to the baptised is a mystery religion. Worship just one god? Defy the emperor? People following the Christian faith, at that time, were being persecuted by the Emperor and singled out for punishment and torture. Christians had to be secretive and in seclusion. For any religion to gain popularity you need participants. A problem was encountered during the conversion to Christianity, however. No matter how good the new religion sounded to the Roman peoples, they were used to their old ways and unique lifestyle. More importantly, they knew how the Gods reacted to these situations, and they trusted Them. There was no reason to switch sides, so to speak, to a god they didn't know, or a religion they weren't familar with.
Taking that into consideration, Christians thought of a plan to make the new converted feel more at ease. They built churches on old worship sites. Their reasoning: people knew the sites, felt comfortable worshipping there and would continue to frequent them, with a building there or not. They incorporated Pagan symbols within the church decor, and added some revised customs to their rituals. To help smooth matters further, they changed the names to some of the deities, called them saints, and added them to the new Christian pantheon.
Sounds easy, right? Well, not really. The Romans were a little upset about all the changes that were happening. They thought that the Christians were making fun of their gods. As a result, most Christians went into hiding for a little while until they could figure out what to do.
So, time passes and around the fourth century, the Christians had a revelation. Unlike other previous religions, Christianity focused on the workings on their god: Jesus, and his death and resurrection. Not much emphasis was placed on his birth. This presented a problem. Because the birth-death-rebirth cycle had been a major part of the Pagan belief system, ignoring the birth aspect became problematic.
Of course, to have a birth you need a woman. Not focusing on the birth of Jesus meant there was no woman, no mother. In Pagan religions there were many goddesses. The Christians needed a goddess. This goddess couldn't been anyone. They needed someone strong and powerful. Deciding on Mary, the mother of Jesus, the early Christians now placed more focus on the birth of their god and Mary became the "Mother of God."
Then came the question of when Jesus was born. The Christians set his birthday on December 25. This date fell in the middle of the winter holidays, and because some Pagans celebrated other festivals around that time anyway, the Christians believed this festival would be relatively unnoticed. They called this festival the "Birth of the Son" and because "son" and "sun" were pronounced the same, the Pagans would think it was just another addition to their festival. Everyone was happy and Christmas was born unto the world!
Source: The History of Yule: How it all began by Dorothy Morrison