Occurrence

The time of sunset varies throughout the year, and is determined by the viewer's position on Earth, specified by longitude and latitude, and elevation. Small daily changes and noticeable semi-annual changes in the timing of sunsets are driven by the axial tilt of Earth, daily rotation of the Earth, the planet's movement in its annual elliptical orbit around the Sun, and the Earth and Moon's paired revolutions around each other. In the summertime, the days get longer and sunsets occur later every day until the day of the latest sunset, which occurs after the summer solstice. In the Northern Hemisphere, the latest sunset occurs late in June or in early July, but not on the summer solstice of June 21. This date depends on the viewer's latitude (connected with the slower Earth's movement around the aphelion around July 4). Similarly, the earliest sunset does not occur on the winter solstice, but rather about two weeks earlier, again depending on the viewer's latitude. In the Northern Hemisphere it occurs in early December (influence from the Earth's faster movement near the perihelion which occurs around January 3).

Likewise, the same phenomenon exists in the Southern Hemisphere, but with the respective dates reversed, with the earliest sunsets occurring some time before June 21 in winter, and latest sunsets occurring some time after December 21 in summer, again depending on one's southern latitude. For one or two weeks surrounding both solstices, both sunrise and sunset get slightly later or earlier each day. Even on the equator, sunrise and sunset shift several minutes back and forth through the year, along with solar noon. These effects are plotted by an analemma.

Why does sunset start getting later before the winter solstice?

It's actually a trick of timekeeping; the days are still getting shorter, but the Sun also RISES later, in addition to setting a minute or two later.

Part of it has to do with the fact that the Earth isn't in a perfectly circular orbit around the Sun; all orbits are elliptical. The Earth reaches its perihelion around January 4 each year, so for the couple of months before then, the Earth is actually speeding up a little in its orbit. Because the Earth is moving (just a little!) faster in December but still rotating at exactly the same speed, the Sun appears to rise and set a couple of minutes earlier than expected.