Meteorites are rocks that come from outer space that somehow manage to make it to the surface of the Earth without completely burning up.While those rocks are falling through the Earth's atmosphere, they experience a partial "burning up" due to their frictional contact with the Earth's atmosphere. This burning action is accompanied by a streak of light that is known as a meteor. When there are many meteors occurring simultaneously, they are collectively called a meteor shower.
Some people poetically call meteors "falling stars" or "shooting stars".
Before these rocks enter the Earth's atmosphere, they are called meteoroids. They consist primarily of debris left in Earth's orbit by periodic comets. They can be as small as dust particles, or significantly larger.
This file succinctly summarized the terms mentioned above. If you would like to see a video of a spectacular meteor, go here.