Solar noon is the time of day when the sun reaches its highest point in the sky, as seen from any particular place on the earth's surface. A solar day is the length of time that passes between solar noon on one day, and solar noon the following day.
The earth takes 23 hours, 56 minutes and 4.09 seconds to spin on its axis. During that time, it also traverses a short distance around its orbit around the sun - approximately one degree of angle - which causes a change in the apparent position of the sun in the sky. In one solar day, the earth must complete an entire rotation on its axis, plus rotate a little more to compensate for that extra (approximately) one degree of angle that the sun appears to move. This little extra rotation takes 3 minutes and 55.91 seconds on average, meaning that the average solar day is almost exactly 24 hours.
However, there are two effects that cause the time taken for the extra rotation to vary substantially. They must both be taken into account, when calculating the length of the solar day. In particular, towards the end of December, the solar days are approximately 25 seconds longer than the annual average.
Seasonal effect on solar days
There is an angle of approximately 23.5 degrees between the plane of the equator and the plane of the earth's orbit. This means that an angle of one degree in the earth's orbit doesn't necessarily correspond to an angle of one degree in the earth's rotation. Close to the solstices (so December and June) this angle between the equator and the orbit implies that to compensate for each degree of the earth's revolution around the sun, the earth must rotate approximately 1.09 degrees. That extra 0.09 of a degree takes the earth approximately 21 seconds. So this has the effect of lengthening the solar days by roughly 21 seconds close to both solstices. Close to the equinoxes (March and September) the opposite effect occurs, and to compensate for each degree of the earth's revolution around the sun, the earth only needs to rotate approxiately 0.92 degrees. This has the effect of shortening the solar days by roughly 20 seconds close to the equinoxes.
Annual effect on solar days
The earth's orbit is not perfectly circular, so generally, it's not travelling exactly at a right angle to the sun. This means that the sun is sometimes pulling against the earth's motion, slowing it down; and sometimes pulling with the earth's motion, speeding it up. The effect is very slight - the earth travels about 1.7% faster than its average when it's closest to the sun in early January; and about 1.7% slower than its average when it's furthest from the sun, in early July. This means that the extra angle that the earth has to make up, from one solar noon to the next, is greatest in December and January, and least in June and July. This has the effect of lengthening the solar days by about 4 seconds at the start and end of the calendar year; and shortening the solar days by about 4 seconds in the middle of the calendar year.
Implication for December's sunrise and sunset times
When calculating sunrise and sunset times, it's necessary to take into account both the time of the solar noon, and the length of the daylight period. Roughly speaking, half of the daylight period occurs between sunrise and solar noon; and half occurs between solar noon and sunset. Now the daylight period is pretty short (for the northern hemisphere) or pretty long (for the southern hemisphere) throughout December, and doesn't vary as much as it does at other times of the year. But the time of solar noon varies a lot, because December has such long solar days.
For about 10 days before the solstice (so typically from 11 to 21 December) the daylight period is getting shorter (northern hemisphere), but so slowly that the long solar days have a greater effect on the time of (northern hemisphere) sunset. So the sunsets move slowly later during this period, even though the daylight period is shortening.
For about 10 days after the solstice (so typically from 21 to 31 December) the daylight period is getting longer (northern hemisphere), but so slowly that the long solar days have a greater effect on the time of (northern hemisphere) sunrise. So the sunrises move slowly later during this perod, even though the daylight period is lengthening.