In reply to Chris the Tall:
Basically what's happening is that the earth's orbit is going through the remnants of a comet tail. It's a bit like the lights in a tunnel they go flashing past on either side which if you trace them back appear to come from a single point. That point, the origin if you like, is called "the radiant". In the case of a meteor shower it's a bit random as to where in the sky a meteor appears and which way it is heading but it's just as likely to be four or five "heading in the same direction" as going off in different directions. Again if you traced the line of the meteors back, even with the "parallel" ones, they will originate from the same region of the sky.
In the current case the radiant is in the constellation of Perseus so the meteor shower is known as the Perseids.
Post edited at 10:30