In the 4th century, church leaders within the Christian churchgoer chose to make the 25th of December the day and night that the feast of Nativity was to be celebrated on. For this occasion, people would fine together, come to good terms with one another and exchange gifts. Again, the date of this celebration was very close to that of the winter solctise and Saturnalia.
The Christmas we are familiar with today developed during the late 18th century and throughout the 19th century. Christmas was then seen as a Christian holiday since the idea of the birth of Jesus on this day came about. So over time, it became celebrated for Jesus rather than the winter solctise and Saturnalia.
During the 20th century, the focus on Christmas became more commercial and people celebrate it either for the religious meanings behind it or to think of others and participate in the time of giving and putting others before themselves. It's now the most celebrated and most popular holiday worldwide.
Sources:
http://www.history.com/topics/Christmas
http://www.simpletoremember.com/vitals/Christmas_TheRealStory.htm
http://www.thehistoryofchristmas.com/
http://www.benbest.com/history/xmas.html
http://x4mr.blogspot.ca/2010/12/christmas-winter-solstice-history.html
