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.
The Quadrantid shower is named after the defunct 19th century constellation Quadrans Muralis. If you trace the paths of the Quandrantids backward, they appear to radiate from a point where this constellation once reigned in the sky.
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.