Why is it that even after Dec. 21, the sunset keeps getting later?

We get a lot of questions asking why, for instance, do the sunsets start to get later in December before Dec. 21. And why the sunrises continue to get later for a period of time after Dec. 21. The same holds true in reverse around June 21.

The explanation is called "The Equation of Time". The best place I've found to explain it is from this NASA Science Article.