All systems in Eve Online contain asteroids (also known as roids) which are grouped together in asteroid belts. They provide the basic building materials by which the vast majority of everything in the game is constructed by. By using mining equipment you can harvest ore from the 16 types currently available. Of these types there are 3 levels of quality for each, with the higher quality asteroids providing an extra 5% or 10% return of minerals after reprocessing in a refinery, so in total there are 48 different kinds of asteroids to be found.
Which types of asteroids you are likely to find in any given system depends on its system security. As a general rule more common (less valuable) ore will be found in a higher Security Status systems and the most valuable ore can only be found in 0.0 (also known as nil sec or null sec). Furthermore, certain asteroids can only be found in certain regions of space.