It's December 21, shortest day of the year.
This doesn't mean earliest sunset. That was back on December 6, Saint Nicholas day. It also doesn't mean latest sunrise--that doesn't come until a week into January. It's just the day where there are fewest hours of daylight.
The shortest day of the year, January 1, and December 25 (Christmas) are actually all supposed to be the same day, or at least have their origin in the idea of the day that darkness has finished getting darker and things will now start returning to light. But they also all have their origin in festivals that humans have held since the beginning of civilization.
The Babylonians, the first astronomers and mathematicians, were also the first to decide that a circle had 360 degrees. They were intensely irritated with the year for having 5 extra days. But this was easily solved. Have a 5-day blowout party with the extra days. (To some extent, our year-end partying is the continuation of this tradition.)
Our calendar is Roman, based on the Julian calendar (of Julius Caesar fame), which was the first to recognize officially that you had to have a leap year every 4 years. (The Babylonians would get around to a leap month every generation or two.) In this calendar, January 1 started the new year, but Saturnalia was a week of feasting and fun leading up to it. (Look how classical we are! Celebrating both with the Babylonians and the Romans!)
In the fourth century, a pagan Roman emperor, disturbed by the rapid spread of Christianity in the Empire, decided to fight back by declaring particular devotion to Apollo, the sun-god, and declared the shortest day of the year the sun-god's birthday--because it was the day he started to increase. In the then Julian calendar, which had been drifting since Caesar's time since no one realized that you can't have leap years on the century (have 24 and skip one), the shortest day of the year was December 25.
The Christians in turn fought back against Apollo and declared December 25 their God's birthday. (The Sun/Son pun only works in English, but it's still applicable.) Christmas has been celebrated then ever since.
Now in fact the New Testament doesn't exactly say that Jesus was born in December. In fact, it puts his birth "when shepherds watched their flocks by night," which would be in the spring, lambing season, when the shepherds have to be vigilant against predators. But it still seems an excellent time for a festival of light and warmth.
For medieval theologians, December 25 also made sense, because the crucifixion took place around the time of Passover according to the New Testament, that is probably late March. And "everyone knows" that important people die on the anniversary of their conception. If Jesus was born on December 25, he must have been conceived on March 25, obviously the date of the crucifixion. It all made sense.