After the Solar System formed, large rocks were left behind called asteroids. These asteroids continue to orbit the Sun.
Near-Earth asteroids are asteroids that have orbits that pass close to Earth. Some of these are called "Earth-crossers", which actually cross the orbit path of Earth. There are currently 7,075 Near-Earth asteroids and about 500 to 1000 of these have a diameter over 1km.
The physical composition of asteroids vary greatly. Some have a rocky core surrounded by an icy mantle. Others, such as one called Vesta are thought have iron-nickel cores.