The shortest day of the year (in the Northern Hemisphere) was our winter solstice, December 21st in the Western Hemisphere (December 22nd from Berlin eastward because of the effect of time zones).
The 21st (or 22nd) is not the earliest sunset, however. In my latitude, about 40 North, the earliest sunset happened December 8th (at 4:28 p.m.). Since then, we've gained over 20 minutes of sun in the afternoon, and we'd already picked up 3 minutes before the 21st.
Not only that, but despite the fact that the (Northern) winter solstice happened on the 21st of December, we did not have our latest sunrise until January 5th, at 7:20 a.m. On December 21st, the sun rose at 7:16 a.m. (4 minutes earlier). In fact, it will not be until tomorrow, January 10, that we pick up our first 1 minute in the mornings.
The cause of these is a phenomenon called the Equation of time.
The earth revolves around the sun at changing speeds, caused by the fact that it has an elliptical orbit. This motion is fastest in December and January, when the earth is closest to the sun.
The speed of rotation (the 24-hour day) cannot change but since, in its course around the sun, the earth moves further than average in December and January, this has the effect of making sunrise and sunset both happen about 1/3 of a minute later each day, cumulatively.
By early December, the north-south movement of the sun, caused by the seasons, is gradually starting to bottom out in a pattern known in trigonometry as a "sine curve." In November, this motion is still making the sunset happen earlier and earlier each day. By early December, however, it flattens out to the point where the seasonal change in the day's length becomes less than one-third of a minute per day.
Meanwhile, the Equation of time is still making everything happen later and later each day. In early December, the point is reached where that 1/3 of a minute per day starts to exceed the fading seasonal change and the sunset seems to start happening later each day.
The reverse happens in the morning. In the first half of December, both the seasonal change and the Equation of time are pulling in the same direction, making the sun rise later each morning. The seasonal movement fades completely by the solstice and even starts to reverse, but the 1/3 of a minute later each day continues to make its presence felt until about January 5th here in New York, when the northward movement of the sun finally wins out and the sunrise starts getting earlier.