The fragment of an asteroid or interplanetary material is known as a meteoroid.
Most meteoroids are small, the size of pebbles or dust from a comet's tail, but they can also be quite large . They are all chunks off of something bigger, sometimes even the moon or a planet like Mars.
If a meteoroid enters the earth's atmosphere, its called a meteor, or shooting star. If it survives the trip through the atmosphere and hits the earth, its called a meteorite. A lot of meteoroids never end up being meteors or meteorites.