This rare complication is usually combined with other astronomical indications. It shows the difference between true solar time and «civilian» time, so-called the apparent and the mean solar time. This distinction is based on your location on the planet, it is always somewhere between plus or minus 15 minutes (ahead around the 3rd November and behind around the 12th February).
As these variations occur identically on the same dates, they can be "programmed" by means of a cam making one complete rotation each year. This complication first appeared on longcase clocks. It was then miniaturized to fit inside a pocket watchcase and later, in the XX century, a wristwatch.
An interesting fact: a big amount of charts and websites include this feature to the short-list of the most useless watch complications; because the knowledge of how much the time on your watch deviates from the true solar time does not actually matter in terms of coordinating with the civilized world's schedule.