Astigmatism is a general inability of the eye to focus clearly at any distance because the curvature of the cornea is not symmetrical. Instead of being spherical, the cornea has more curvature in one meridian than the other. In other words, the eye's main focusing element has two curvatures, shaped like a football instead of a basketball.
Nobody has a perfectly symmetrical cornea, but the distortion is so slight in most eyes that it does not significantly affect vision. However, possessing more than a slight degree of astigmatism can be a major refractive problem. Astigmatism is often combined with myopia and hyperopia.
This illustration shows only one of the many possible variations of astigmatism.