December Solstice is the phenomenon which makes the 21st December special because it is also an astronomical event. Dec-21 is the shortest day and the longest night of the year in the northern hemisphere and shortest night and the longest day of the year in the southern hemisphere.
Reason of the longest night of the year in Northern hemisphere
This phenomenon is caused due to a tilt of the axis of rotation of the earth with respect to the plane of revolution around the sun by 23.5°. During December solstice the sun reaches its most southern declination of -23.5°. Sun is directly overhead on the tropic of Capricorn in the southern region during the December solstice. On these days, the northern hemisphere is at the farthest distance from the sun and southern hemisphere is fully exposed to sun rays. This situation corresponds to summer in southern hemisphere and winter in the northern hemisphere.
Effect on the day length in the Northern and Southern hemisphere
In the region between the latitude of 23.5°N (tropic of cancer) and 66.5°N (arctic polar circle) the day length is shortest and night length is largest. But between the arctic polar circle and the North Pole, the sun does not rise so there is full night throughout the day. In the southern hemisphere between Tropic of Capricorn and Antarctic polar circle, everything opposite happens like largest day and smallest night. Also between Antarctic polar circle and the South Pole, the day length is 24 hours; it means the sun glows in the midnight also.
Effect on the day length in region around the Equator
In the region between 23.5°N and 23.5°S, there is not much difference between the day and night length but still days are longer for the region between the equator and 23.5°S and shorter for the region between the equator and 23.5°N as compared to night during December solstice.
June Solstice causing the longest day of the year in Northern hemisphere
A totally opposite phenomenon happens during June solstice which happens during 20th and 21st June. During June solstice sun is present overhead on the tropic of cancer (north) causing the shortest night and the longest day of the year in the northern hemisphere and the shortest day and the longest night of the year in the southern hemisphere. June Solstice also corresponds to summer in northern hemisphere and winter in the southern hemisphere.