When they enter our atmosphere they start to burn, and are called meteors. Meteors streak across the sky, blazing bright for only a few seconds. As the Earth moves in its orbit around the Sun, it occasionally crosses the stream of dust left by a comet, and this causes a meteor shower. Sometimes meteors are large enough to survive the fiery trip through the atmosphere, and actually hit the ground. These are called meteorites.
Most meteorites are small and they cause very little damage when they hit.
There are only two documented cases of a person being hit by a meteorite. Comets are also chunks of rock, but they have ice mixed in as well. They have very long orbits, and when they come close to the Sun, the heat boils off frozen ice from them, and pushes it into a long, bright tail. Comets are much bigger than meteors and they do not have to enter our atmosphere to be seen. Comets can be seen for many weeks as they move slowly across the sky.