This marks the beginning of winter (in the northern hemisphere) and the beginning of summer (in the southern hemisphere.) The winter solstice is the shortest day of the year, respectively, in the sense that the length of time elapsed between sunrise and sunset on this day is a minimum for the year. Of course, daylight saving time means that the first Sunday in April has 23 hours and the last Sunday in October has 25 hours, but these human meddlings with the calendar and do not correspond to the actual number of daylight hours.
If you life in the southern hemisphere, this is your Summer Solstice, celebrating the longest day of the year.
http://scienceworld.wolfram.com/astronomy/WinterSolstice.html
The Quadrantids is an above average shower, with up to 40 meteors per hour at its peak. It is thought to be produced by dust grains left behind by an extinct comet known as 2003 EH1, which was discovered in 2003. The shower runs annually from January 1-5. It peaks this year on the night of the 3rd and morning of the 4th. The first quarter moon will set shortly after midnight, leaving fairly dark skies for what could be a good show. Best viewing will be from a dark location after midnight. Meteors will radiate from the constellation Bootes, but can appear anywhere in the sky.
Part of the Moon will appear darker as the full Moon passes through the faint outer edge (penumbra) of the Earth’s shadow.