Although there is no doubt that the day with the least total amount of daylight is December 21st (the winter solstice), the earliest sunset of the year actually occurs on December 8th.
The reason has to do with something called the Equation of Time and depends on the tilt of the earth and the shape of its orbit around the sun. You can read the detailed explanation of why here.
Although the time the sun sets will be getting later from now on until the summer, the sunrise will continue to be later and later until early January. Also remember that at this time of the year there is usually only a few seconds to a minute difference between the sunrise and sunset times from day to day. So by the end of the month the sunset will only be about 10 minutes later than it is today.