The Asteroid Ida. Its moon Dactyl is on the right.
Asteroids are the rocky, broken remains of planetesimals, which were bodies that never grew large enough to become planets. Asteroids are mostly found in the asteroid belt, between Mars and Jupiter.
Meteoroids are small pieces of asteroids. When meteoroids enter Earth's atmosphere they become meteors, or shooting stars. Most meteors burn in the mesosphere, but some make it to the ground, and become meteorites. A meteor shower occurs when a lot of meteors enter the atmosphere at the same time.