Falling stars are meteors, usually not much larger than a grain of sand. They enter Earth's atmosphere at several miles per second and burn up.
It's always amazed me that we could even see something as small as that burning up when it's so darned far away from us (what, five, ten or even twenty miles over our heads?). So, they miss Earth in the sense that they do not make it to the ground, but they definitely hit Earth's upper atmosphere (and that's no miss in my book!).
Astronomers don't call them asteroids or comets, reserving those designations for larger stuff.
BTW, I'm not an astronomer/physicist either, just a guy who's had a couple of astronomy courses. :-)
Lots of people still laugh when there is talk of setting up an asteroid defence system. The chances of a big hit are small but there's always that chance, the planets have swept up most of the rocks flying round the solar system but there will always be rocks out there.
Actually, what is seen is the ionization of the atmosphere.