The Geminid meteor shower, which is due to peak on the night of Thursday, December 13th at an average of 120 meteors per hour, doesn't originate from a comet like nearly every other meteor shower does, but instead is due to a rocky object known as 3200 Phaethon (FAY-eh-thon). 3200 Phaethon was first discovered in 1983 by UK astronomers Simon Green and John Davies, and confirmed shortly thereafter by American astronomer Charles Kowal, who described it as 'asteroidal'. Tracking the object and computing its orbit, astronomers found that it matched the trail of debris the Geminids are caused by so closely that they couldn't reach any other conclusion — it had to be the source of the Geminid meteors.
Two hypotheses exist to explain how this rocky object could create a meteor shower.
Studies of the 3200 Phaethon have shown that it very closely matches the composition of a minor planet called 2 Pallas, which orbits the Sun inside the solar system's asteroid belt. This means that 3200 Phaethon could be a large chunk of Pallas that was fragmented off in a collision, and the Geminid meteors are caused by dust and debris from that collision trailing behind the object as it orbits the sun.
Another possibility, though, is that 3200 Phaethon is an entirely new kind of object called a 'rock comet' — an asteroid that spends part of its orbit very close to the Sun, where the intense heat burns off layers of dust and debris from the surface of the rock.
Looking to test this idea, astronomers used NASA's Solar Terrestrial Relations Observatory (STEREO). These two satellites, which have been set up in solar orbit — one moving increasingly farther ahead of the Earth and one lagging further and further behind — are designed to allow us a continuous observation of the Sun, including the side that is opposite to our view. These two satellites took images of 3200 Phaethon in 2009 as it made its closest approach to the Sun, and observed that on May 19th, the object brightened significantly. Examining the data in relation to all the possible ways that this could have happened, the astronomers concluded that this increased brightness must have been caused by 3200 Phaethon throwing off a large amount of dust, which then reflected sunlight, just as what happens when a comet approaches the Sun.
The amount of brightening that they saw doesn't seem to account for the number of meteors we consistently see from the Geminid meteor shower, however it is possible that — if 3200 Phaethon is a rock comet — its surface may have been much more unstable (possibly having a higher water and ice content) in the past than it is today, thus it would have produced larger amounts of dust on its close passes by the Sun.
The only other meteor shower thought to originate from something other a comet is the Quadrantid meteor shower, in early January. In 2003, Dutch astronomer Petrus Jenniskens suggested that the source for the Quadrantids may be the minor planet 2003 EH1, which might be the same object as comet C/1490 Y1, which was observed by east Asian astronomers over 500 years ago.
For best viewing of the Geminids, try to get away from as much city light pollution as possible and look towards the east-northeast starting about an hour or so after sunset. This year should be exceptionally good, because that night happens to be a New Moon, meaning that there will be no lunar 'light pollution' to spoil the show.