SOL INVICTUS ("the Unconquered Sun") or, more fully, Deus Sol Invictus ("the Unconquered Sun God") was the late Roman state sun god. The cult was created by the emperor Aurelian in 274 CE and continued until the abolition of paganism under Theodosius I. The Romans held a festival on December 25 called Dies Natalis Solis Invicti, "the birthday of the unconquered sun."
The use of the title Sol Invictus allowed several solar deities to be worshipped collectively, including Elah-Gabal, a Syrian sun god; Sol, the patron god of Emperor Aurelian (270-274); and Mithras. Oh, and a Jewish upstart named Jesus.
December 25th was also considered to be the date of the winter solstice, which the Romans called bruma. It was therefore the day the Sun proved itself to be "unconquered" despite the shortening of daylight hours. (When Julius Caesar introduced the Julian Calendar in 45 B.C.E., December 25th was approximately the date of the solstice. In modern times, the solstice falls on December 21st or 22nd.)
The Sol Invictus festival has a "strong claim on the responsibility" for the date of Christmas, according to the Catholic Encyclopedia. Solar symbolism was popular with early Christian writers as Jesus was considered to be the "sun of righteousness."
The date for Christmas may also bear a relation to the sun worship. According to the scholiast on the Syriac bishop Jacob Bar-Salibi, writing in the twelfth century:
"It was a custom of the Pagans to celebrate on the same 25 December the birthday of the Sun, at which they kindled lights in token of festivity. In these solemnities and revelries the Christians also took part. Accordingly when the doctors of the Church perceived that the Christians had a leaning to this festival, they took counsel and resolved that the true Nativity should be solemnized on that day." (cited in "Christianity and Paganism in the Fourth to Eighth Centuries", Ramsay MacMullen. Yale:1997, p155)