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Velocity and Atmosphere
As an asteroid enters the atmosphere, the Earth's gravity causes the the object's velocity to increase while the air molecules in the sky simultaneously slow the object down, causing a friction that results in increased heat as well as a large amount of energy being let out from the object. That increased heat and energy release causes the asteroid to burn up, melt and vaporize in the atmosphere.
Size
An asteroid's size determines its survival in the atmosphere. For example, much of the material entering the atmosphere are dust-like micrometeorites, but these objects don't actually burn up but slowly float down to the ground. Objects smaller than around 2 cm vaporize in the atmosphere, but objects larger than 2 cm tend to only slightly burn up, which results in the surviving objects making impact with the ground. If an object is big enough, the atmospheric friction resulting from entry into the atmosphere won't have an effect on the object's velocity.
Burning
As the object burns up in the atmosphere, the heat ionizes the gas in the atmosphere, creating a bright, visible light larger than the object itself that moves through the sky along with it. As a result, one of the common names for burning objects in the sky is "shooting star" or "fireball" if the light is particularly bright.
After the Burning
Occasionally, a rock will survive the process of entering Earth's atmosphere if its velocity is low enough and its size large enough. The atmosphere will slow it down to a certain point as it cools off and the object, often called a meteorite, impacts the earth. This meeting of meteorite and ground creates a crater called an impact crater. However, depending on where it lands, it could also cause property damage or even bodily injury. This is especially true of objects larger than 1 km, which, upon impacting the planet, can cause great damage.