Asteroid belts are very common in EVE. They are places located within most star systems, filled with asteroids, commonly visited for mining or ratting. Asteroids (floating chunks of rock, ice, or metal) are mined for minerals. Over time they can be mined out, but they will be reset often. Asteroid belts are also frequented by NPC pirate ships, known as "rats", which while annoying to miners are a prey for more combat oriented players.
Asteroid belts become better and better value wise as you move into lower security.