Asteroids are distinguished as small solar system bodies that orbit a sun. Specifically, we consider small planetoids that orbit around our sun to the distance of Jupiter to be asteroids. Asteroids are usually rocky or metallic. Their composition varies greatly from one asteroid to the next. Due to their orbit in the solar system many astronomers prefer to call asteroids ‘minor planets’.
Many asteroids are believed to be the remnants of planetesimals. A planetesimal is the growing aggregation of cosmic dust from such things as the disintegration of red stars caused by stellar winds. When the dust collection reaches about 1 km wide the mass has strong enough gravitational forces to hold itself together and to continue binding into a bigger mass that assumes a stable orbit.
Most asteroids in our solar system are located around Jupiter. It is believed that most asteroids were formed near Jupiter. This distinguishes asteroids from comets which are formed often farther out in the solar system. Moreover, comets have a red tail or coma. When the comet becomes extinct and loses its red coma it is possible to describe it as an asteroid.
Although most asteroids are found between Jupiter and Mars with non-eccentric orbits (not elongated) there are a few that pass close to the Earth. These are known as Near-Earth Asteroids or NEAs. How dangerous are NEAs? That is a matter of orbit and mass. In 2010, 7,075 NEAs were listed, of these 500 to 1,000 are believed to be 1km or over in diameter. These are the near-Earth Asteroids that we have to keep tabs on.
Further reading: Stars and Carbon