The above photo shows the meteor shower in the early hours of this morning (Fri 14 Dec 2012) just SW of Brisbane facing W. Lots of satellites were also captured (the long streaks). The photo is a composite image of activity between 3 - 4am. The blue trails represent meteors and satellites that occurred as the sky brightened at dawn.
A meteor shower occurs when the earth drifts through the tail of a comet. Dust, ice and debris from the comet's tail plough into the earth's atmosphere and burn up, leaving fire trails across the sky like shooting stars. The intensity of the shower depends on the location of the comet in its orbit around the sun and how close we are to it. The showers are named not after their parent comet, but after the constellation that the shower appears to emanate from in the sky.
There's some great info on the Geminids here.