solstice basically means "sun stopping" or "sun standing." It is like the word armistice has the same Latin root and means "arms standing."
A solstice is not a day. It is the time that the Sun reaches it's most northern (summer) or southern (winter) point. The Sun is directly overhead of the Tropic of Capricorn in the Southern Hemisphere during the Winter Solstice.
Today that will be at 3:03 P.M. Pacific Standard Time. So you can adjust to your time zone. For example, that's 6:03 P.M. Eastern Standard Time.
If you are north of the Arctic Circle, there will be at least one day around the Winter Solstice when the sun does not rise over the horizon. The farther north you are, the more days that is and at the North Pole, it's six months. Conversely, in the summer, there will be at least one day when the sun does not set and the farther north you are the more days there will be. Again, at the North Pole, that's six months of daylight.
When I was growing up in Southeast Idaho at an elevation of nearly 4,500 feet, winter (as signified by the first snow) started late October. It struck me as strange that the first official day of winter was essentially in the middle of winter. And spring, which starts about March 22nd officially, was still, in winter ("winter" ran from late October to early April).
People mistakenly called the day of the Winter Solstice "the shortest day of the year" when what they mean is it's the shortest daylight of the year. Where I live, sunrise was at 7:41 this morning and sunset will be at 4:09 this evening. That's 8 hours and 28 minutes of the sun being up (if my math is correct). And miracle of miracles, it's actually a sunny day here.
So why is Christmas on December 25th? One theory holds that most cultures have a post Winter Solstice party. They've been watching the Sun get lower and lower in the sky, the day light get shorter, the temperatures get cooler. Somebody's gotta be thinking "If this goes on, we're doomed."
Then it stops, the periods of daylight start getting longer again. So hey, let's have a big party! And since Christmas was scheduled by early Christians to coincide with Saturnalia, which was probably started as one of those parties, that's why Christmas is three days (about) after the Winter Solstice.