For Northern Hemisphere observers, the winter-solstice Sun appears at its southernmost point in the sky.
At the December solstice, Earth's Northern Hemisphere is tilted farthest away from the Sun. The Sun's apparent path therefore reaches its lowest daily arc and its southernmost declination, about 23.4° south of the celestial equator.
This produces the Northern Hemisphere's shortest day and longest night. At noon, the Sun is lower than on any other day of the year, although its exact altitude depends on the observer's latitude. The effect is reversed south of the equator, where December brings the summer solstice.
“Southernmost” describes the Sun's north-south position on the celestial sphere, not the direction of sunset. The Sun still rises generally in the east and sets generally in the west, with the precise points shifting seasonally.