Under the Julian calendar of the Roman empire, the Winter Solstice fell on December 25th.
As the shortest day of the year, December 25th had a special significance as a time of rebirth, given that it was the day when the days began getting longer. Accordingly, ancient peoples in Europe often marked the Winter Solstice with ebullient festivals, such as the one honoring the Invincible Sun. Although the early Church (and later groups like the Puritans) attempted to ban the celebration of the Winter Solstice, ultimately, they gave in and attempted to graft a Christian meaning upon it, which wasn't too hard since the Christian God Jesus also was highly symbolic of rebirth.
Placing the celebration of Christ's birth on the Winter Solstice set things up nicely to coincide with placing the celebration of his death and resurrection during the Spring festivals, aka Easter (from the word for the old German moon goddess and related to the modern word estrogen), which often celebrated the death and rebirth of the spouse of the moon goddess.
The Julian calendar was later superseded in the middle ages and the Winter Solstice fell back to around the 22nd day of the year, although December 25th continued to be the date upon which the pagan winter holiday/Christmas continued to be observed.
So the next time one of those fundamentalist busybodies talks about "putting the Christ back into Christmas," tell him that Christ never was in Christmas to begin with and to get their own holiday.