A short explanation that defies the regularly suggested theory that Christians mimicked the Roman holiday of Saturnalia.
The answer to a lot of questions about why Christians do the things they do is often "because the Romans did." However, contrary to a lot of opinions on the matter, this is not how December 25th was chosen to be the day that most Christians celebrate the birth of Jesus.
Certainly, the Romans had their festivals during this time of year. They celebrated Saturnalia, in honor of the god Saturn, during the third week of December. Celebrations included sacrificing a pig, gambling, role-reversals, transvestism, overeating, drunkenness, and nudity.
While some of these traditions might seem pretty commonplace during the holiday season today, the early Christians, particularly Jewish Christians, were a more scrupulous lot and viewed participation in such revelries as contrary to the obligations of their faith. The Romans were generally tolerant of other religions, except when it came to Jews and Christians who stubbornly refused to offer sacrifices to their pagan deities and deified Roman emperors. The blood of thousands of martyrs testifies to this. The assertion by some historians that Saturnalia was co-opted by Christian leaders just for the gift-giving tradition is absurd.
While some of these traditions might seem pretty commonplace during the holiday season today, the early Christians, particularly Jewish Christians, were a more scrupulous lot and viewed participation in such revelries as contrary to the obligations of their faith.
The real explanation is much simpler. While there is no reliable evidence about when Jesus was actually born, there was a long tradition that if a man lived a perfect life, he would die on the day that he was conceived. Early Christians believed that Jesus was crucified during the Passover ca 33 A.D. The date, based on the Jewish lunar calendar, was believed to be March 25th, which today is celebrated as the day that the angel Gabriel appeared to the Virgin Mary and announced that she would conceive a son. Nine months from that day, she would have given birth, hence, December 25th.
While there is no reliable evidence about when Jesus was actually born, there was a long tradition that if a man lived a perfect life, he would die on the day that he was conceived.
Additionally, before Emperor Constantine made December 25th the first official Christmas Day in 336 A.D., many eastern Christians celebrated January 6th as the day that the Magi arrived in Bethlehem bearing gifts to the newborn Christchild. The switch from the Julian calendar to the Gregorian calendar in 1582 took ten days off the new calendar and brought that day to the day after Christmas.
Another Christian tradition emerged later that bears some resemblance to the Roman celebrations of "Sol Invictus," the Unconquered Sun, and the eastern god of light, Mithras. The third week of December, of course, marks the time when the days start getting longer again. Luke writes that Mary went to see her cousin Elizabeth, who (on March 25th) was six months pregnant with John the Baptist. That would put John's birth three months later, ca 24 June--around the summer solstice time when the days start getting shorter. Reflecting on this, early Christians recalled the later words of the Baptist that his light "must decrease" while Christ's sun, so to speak, must increase.