There are two schools of thought on this.
Some scholars suggest that Christmas occurring on December 25 was meant to allow Christmas to easily replace a celebration of the Roman sun god Sol Invictus. Others have suggested that Christmas predates the celebration of Sol Invictus and that the celebration of Sol Invictus was meant to eclipse the Christmas holiday, although few records have survived from the time of Roman persecution of Christians under Emperor Aurelian to support this.
St. Hippolytus, who was already knowledgeably defending the faith in writing at the turn of the century, entering the 3rd century AD, said that Christ was born Wednesday, December 25, in the 42nd year of Augustus’ reign (see his Commentary on Daniel, circa AD 204, Bk. 4, Ch. 23).
Additional calculations are made based on the six-year almanac of priestly rotations, found among the Dead Sea Scrolls. Some believe that this almanac lists the week when John the Baptist’s father served as a high priest. As it is implied that John the Baptist could only have been conceived during that particular week; and as his conception is believed to be tied to that of Jesus, it is claimed that an approximate date of December 25 can be arrived at for the birth of Jesus.