Answer:
All the meteors in a meteor shower typically come from the same comet, which is in a periodic orbit around the Sun. The dust from the comet follows the path of the parent body and as Earth intersects the debris along the comet's orbit, it plows into this material. Since the dust particles are all moving together in space before they encounter Earth, if you trace back the streak of each meteor, its path will appear to diverge from one place in the sky.
