Astigmatism occurs when the eye has different refractive power in different meridians.
This is commonly explained by way of analogy, in that the cornea is shaped more like a rugby ball than a football, with steeper curvature in one direction than the other.
Astigmatism can occur alongside emmetropia, hypermetropia or myopia.
Source: National Eye Institute, National Institutes of Health
Correction
Astigmatism is corrected using a lens which has different powers along different meridians. This allows the multiple focus points to be brought to a sharp focus on the retina.