Most shooting stars come from dust floating in space. The Earth is orbiting the sun at a very high speed -- something like 66,000 miles per hour (over 100,000 kph). When the Earth runs into the dust in space, the dust particles streak through the atmosphere and heat to the point where they incandesce -- they give off bright light as they burn up in the atmosphere, and we see the light as a shooting star.
Discussing meteor activity can be tricky because the terminology is confusing. The term meteor actually refers to the streak of light caused by a piece of space debris burning up in the atmosphere. The pieces of debris are called meteoroids, and remnants of the debris that reach the Earth's surface (or another planet's) are called meteorites.
Meteoroids have a pretty big size range. They include any space debris bigger than a molecule and smaller than about 330 feet (100 meters) -- space debris bigger than this is considered an asteroid. But most of the debris the earth comes in contact with is "dust" shed by comets traveling through the solar system. This dust tends to be made up of very small particles.
So how can we see a meteor caused by such a small bit of matter? It turns out that what these meteoroids lack in mass they make up for in speed, and this is what causes the flash of light in the sky.
Meteoroids enter the atmosphere at extremely high speeds -- 7 to 45 miles per second (11 to 72 kilometers per second). They can travel at this rate very easily in the vacuum of space because, it being a vacuum, there's nothing to stop them. The Earth's atmosphere, on the other hand, is full of matter. As a meteoroid moves through the atmosphere, this matter compresses in front of it. This compression generates enough heat (up to 3,000 degrees Fahrenheit, or 1,649 degrees Celsius) to raise the meteoroid's surface to its boiling point, so the meteoroid is vaporized, layer by layer, as it moves through Earth's atmosphere.
The extreme heat breaks the molecules of both the meteoroid material and the atmosphere into glowing ionized particles, which then recombine, releasing light energy to form a bright "tail." A meteor tail caused by a grain-sized meteoroid is a only a few feet (about a meter) wide but, because of the high speed of the debris, may be many miles long.