The Quadrantids are named after the obscure constellation Quadrans Muralis, the Mural Quadrant, depicted in some 19th-century star atlases near where Draco, Boötes, and Hercules now meet. The figure was invented in 1795 by Joseph J. Lalande to commemorate the instrument used to observe the stars in his catalog. It was removed in the 1920s when the International Astronomical Union adopted the modern list of 88 officially recognized constellations. Most of Quadrans Muralis ended up in Boötes, but the meteor shower kept its name, likely because there's already a minor shower emanating from Boötes during January — the Bootids.
The shower's origin is a small, recently discovered asteroid-like body, according to meteor expert Peter Jenniskens (NASA/Ames Research Center). The source is a chunk of rock just a couple of kilometers wide found in March 2003 and designated 2003 EH1. It has an odd, high-inclination orbit that matches the orbit of the Quadrantids when both are tracked back through several centuries of planetary perturbations. Jenniskens estimates that the Quadrantid meteoroids we encounter today left 2003 EH1 only about 500 years ago. The association of 2003 EH1 with the Quadrantid stream identifies it as a dead short-period comet, much like the "asteroid" 3200 Phaethon, source of the Geminid shower.
The “Quads” typically have a very sharp peak lasting only a few hours. But if you’re watching when it arrives, this can be one of the year’s best meteor displays.