Every year, I hear people talk about where Christmas came from. Here are two discussions of how there came to be a celebration of Jesus’ birth on December 25.
From Philip Schaff, in his History of the Christian Church:
The Christmas festival was probably the Christian transformation or regeneration of a series of kindred heathen festivals—the Saturnalia, Sigillaria, Juvenalia, and Brumalia—which were kept in Rome in the month of December, in commemoration of the golden age of universal freedom and equality, and in honor of the unconquered sun, and which were great holidays, especially for slaves and children. This connection accounts for many customs of the Christmas season, like the giving of presents to children and to the poor, the lighting of wax tapers, perhaps also the erection of Christmas trees, and gives them a Christian import; while it also betrays the origin of the many excesses in which the unbelieving world indulges at this season, in wanton perversion of the true Christmas mirth, but which, of course, no more forbid right use, than the abuses of the Bible or of any other gift of God.
Had the Christmas festival arisen in the period of the persecution, its derivation from these pagan festivals would be refuted by the then reigning abhorrence of everything heathen; but in the Nicene age this rigidness of opposition between the church and the world was in a great measure softened by the general conversion of the heathen. Besides, there lurked in those pagan festivals themselves, in spite of all their sensual abuses, a deep meaning and an adaptation to a real want; they might be called unconscious prophecies of the Christmas feast. Finally, the church fathers themselves confirm the symbolical reference of the feast of the birth of Christ, the Sun of righteousness, the Light of the world, to the birth-festival of the unconquered sun, which on the twenty-fifth of December, after the winter solstice, breaks the growing power of darkness, and begins anew his heroic career. It was at the same time, moreover, the prevailing opinion of the church in the fourth and fifth centuries, that Christ was actually born on the twenty-fifth of December; and Chrysostom appeals, in behalf of this view, to the date of the registration under Quirinius (Cyrenius), preserved in the Roman archives. But no certainty respecting the birthday of Christ can be reached from existing data.
From Craig Blomberg, in his Jesus and the Gospels: An Introduction and Survey:
In post-New Testament times, Mithraism (originally from Persia) amalgamated with the Roman worship of Sol Invictus (the unconquerable sun), and a festival to Sol was celebrated every December 25. Christians took advantage of this “day off” to protest against Mithraism by worshiping the birth of Jesus instead. After the Roman empire became officially Christian (fourth century), this date turned into the legal holiday we know today as Christmas. The celebration of the annual death and rebirth of the nature gods finds parallels and contrasts, too, with Christian teaching about the death and resurrection of Christ (34).
It is important to note that Christmas did not start out as a pagan festival. It was the co-opting of a pagan festival. In this way, it is like Festivus, the holiday that Frank Costanza (A character on the TV show Seinfeld) created as an alternative to Christmas. There was already a holiday being celebrated, and Christians used the festive atmosphere to create their own holiday.