Asteroids are bits of rock that fly around the Solar System. Sometimes they orbit the Sun but sometimes they just break off something else (usually a planet) and fly off. Depending on various factors, they might be captured into a Sun orbit, but they might just fly out of the Solar System altogether, never to be seen again.
Asteroids regularly impact with the Earth, but are either burn up in the Earth's atmosphere, or are insignificantly big to do anything to the Earth. However, it is speculated that several large asteroids have hit the Earth with enough force to do stuff in the past. One popular theory is this is how dinosaurs were wiped out