In the Northern Hemisphere, winter is held to begin on the day of the Winter Solstice, the day (actually a moment in time) when the position of the sun reaches its most southerly limit before slowly beginning to move north again. The Winter Solstice also marks the shortest day and longest night of the entire year. (For dwellers in the Southern Hemisphere, the situation is reverse: the solstice which occurs in December is their Summer Solstice, and marks their longest day and shortest night of the year.)
In our modern Gregorian Calendar (which is a 16th century slight modification of the Julian Calendar, established way back in the time of Julius Caesar), the Summer Solstice falls, in any given year, on a date as early as December 20 and as late as December 23. The shifting of the sun’s apparent position throughout the year is caused not by any actual motion of the sun itself, but rather is the result of an effect created by the fact that earth’s axis is not perpendicular to the plane of its orbit around the sun but is tilted at an angle of a little more than 23 degrees. This means that, for one half (six months) of the earth’s annual journey around the sun, one hemisphere is pointed more directly at the sun than the other, and then they trade places at the Equinoxes. (In the Northern Hemisphere, the Equinox occurring in the month of March is called the Vernal Equinox, and the one occurring in the month of September is called the Autumnal Equinox.) The hemisphere receiving more direct sunlight (and for a longer portion of each 24-hour day) experiences summer, and the hemisphere receiving less direct sunlight (and for a shorter portion of each 24-hour day) experiences winter.
Just how short the day is compared to the night on the Winter Solstice depends on your latitude (how far north or south you are on the earth’s globe, as measured from the equator). For those dwelling in the lower 48 states of the US, the daylight period on the Winter Solstice ranges from about 10 hours (southern states around the Gulf of Mexico) to about 8 hours (northern states close to the Canadian border). And for those living in the extreme north, the day is a very short one indeed (if the sun rises at all): the sun is below the horizon for at least 24 hours on the Winter Solstice for any location within the Arctic Circle (about 66 degrees north latitude), and at the North Pole itself, the Winter Solstice marks the mid-point of a six month period of darkness, during which the sun never rises above the horizon!
If you mark where the sun rises each morning as seen from exactly the same location during the course of a year, you will find that its rising points at Winter Solstice and Summer Solstice are separated (again, using latitudes for the lower 48 states of the US) by anywhere from about 50 to almost 70 degrees. So, for example, if you have live on a quarter acre lot that is oriented on a roughly east-to-west axis, from a given spot on your porch or from a given east-facing window of your house, you will probably see the sun rise from somewhere beyond the southeast corner of your yard on the Winter Solstice, and somewhere beyond the northeast corner on the Summer Solstice. If you mark the position carefully from one day to the next, you’ll also notice that the south-north movement is most rapid at the middle of the cycle (during the time around the equinoxes) and is slowest at either end (at the solstices). This is similar to the effect of tossing a ball into the air and catching it again: the ball is traveling fastest when it leaves you hand and just before it lands in your hand again, and as it reaches the top of its path, it slows, appears to stop and hover for a brief moment, and then slowly starts to fall, gaining speed as it descends. (The word solstice, in fact, comes from a Latin compound which means “stopped sun.”) This also means that while the Winterer Solstice is indeed the shortest day of the year, it is only a minute or so shorter than the day before and the day after. In fact, the difference in length of daylight from one day to the next is only very slight for several weeks before and after the Solstice, and daylight hours run very short throughout the entire period. (The difference becomes more noticeable during the time surrounding the equinoxes.)
One commonly held (though false) assumption about the Winter Solstice is that it also marks the latest sunrise and earliest sunset of the year. This is not the case: due to the complicated nature of astromechanics, these events actually lag behind (latest sunrise) or ahead of (earliest sunset) the Winter Solstice by several days.
In ancient times, the Winter Solstice was regarded in many northern European cultures not as the beginning of winter, but rather as winter’s mid-point. For this reason, the Winter Solstice and the surrounding period of time is often referred to as “Midwinter,” especially in older literature. The Germanic peoples of northern Europe (including the Anglo-Saxons) observed a weeks-long winter celebration known as Yule or Yuletide between mid-November and early January, culminating in a 12 day feast which began on the Winter Solstice (which in the days of the Julian Calendar was reckoned as December 25th). As Europe became Christianized, the older pagan rituals were supplanted by the celebration of Christmas, though vestiges of older Yuletide traditions still remain and are alluded to in many a Christmas carol.