Because the Winter Solstice is a celestial event, it takes place on different days of the calendar, depending on the year, varying between December 21 and December 23. You can see a list of the days and times of the solstices and the equinoxes here at this Hermetic Systems webpage. Moreover, this is a hemisphere-specific holiday: December marks the Winter Solstice in the northern hemisphere, but in the southern hemisphere, it is the Summer Solstice.
There are many cultures which celebrate a special ritual on the occasion of the Solstice, often based on the symbolism of light and its triumph over the night. Yesterday, I posted about the Iranian festival of Yalda. You can find a long list of Winter Solstice celebrations in many cultures listed in this Wikipedia article.
There are many connections between Christmas celebrations and the Winter Solstice. The Gregorian calendar puts the Winter Solstice between December 21 and 23, but in the old Julian calendar the Winter Solstice took place around December 24, in other words, at Christmas. Over time, the Gregorian and Julian calendars have diverged farther and farther; to see this difference calculated, you can use this fascinating Calendar Calculator.
In northern Europe, the traditional winter solstice celebration was called Yule, which is a word many people associate today with Christmas. Yule traditions include decorating a fir tree, making decorations of mistletoe and holly, gift-giving and merry-making. The Yule log tradition takes different forms in different cultures, such as the Tió de Nadal in Catalonia, or the yummy Bûche de Noël pastry.
Another word for the Yule festival is Midwinter, like the corresponding Midsummer fesitval which takes place at the Summer Solstice. You can see this relationship clearly in the Wiccan Wheel of the Year, where Yule (Midwinter) and Misummer are opposite one another.
We're celebrating the Winter Solstice with some friends tonight, and here is a selection of Winter Poems we will be reading: enjoy!