So, here's the deal. Comets leave a trail of dust as they travel through space. Our planet passes through that dust trail on our journey around the sun. Those dust particles create a brilliant trail of their own as they hit our planet's atmosphere and heat up. They get so hot they burn and are destroyed. Only large meteors ever hit the surface. Generally comets only leave small particles the size of a grain of sand. This meteor shower is called the Leonid's because it appears the dust particles are coming from the constellation Leo in the eastern sky.
There are several websites that describe it far better than me. But really, if it's not cloudy tonight look up. The magic of something so small making such a beautiful trail of light is something you need to see...more than once.