While most meteor showers are associated with comet trails, Geminids seems to be a mystery. I've read that it could be a chip off asteroid Vesta and then there's this article from Spaceweather.com

The source of the Geminid shower is an object called 3200 Phaethon. Discovered in 1983 by NASA's Infrared Astronomical Satellite, Phaethon shares its orbit with the Geminid meteoroids. Furthermore, it is about the right size to be a comet. So far, so good...
But 3200 Phaethon doesn't act like a comet, says Cooke. "3200 Phaethon doesn't sprout a tail when it comes close to the Sun. It doesn't have a halo or a coma ... in fact, based on its orbit and the way it reflects sunlight, it seems much more like an asteroid."

More on NEA Phaethon's orbit at Science@NASA along with explanation and photos.

Either way Geminids offer the chance to see meteors without having to stay up all night.

SteveS