In the United States and the rest of the northern hemisphere, the first day of the winter is the day of the year when the Sun is fartherst south on December 22nd. This day is known as the Winter Solstice.
The declination of the Sun on the winter solstice is known as the tropic of capricorn (-23 degree 27″). In the Southern hemisphere, winter as summer solstices are exchanged so that the winter solstice is the day on which the Sun is farthest north.
A common misconception is that the earth is further from the sun in winter than in summer. Actually, the Earth is closest to the sun in December which is winter in the Northen hemisphere.
As the Earth travels around the Sun is it orbit, the north-south position of the Sun changes over the course of the year due to the changing orientation of the Earth’s tilted rotation axes. The dates of maximum tilt of the Earth’s equator correspond to the Summer Solstice and Winter Solstice, and the dates of zero tilt to the Vernal Equinox and Autumnal Equinox.