Astigmatism simply means having morethan one point of focus. (Short-sighted with astigmatism or long-sighted with astigmatism). This happens when the surface of the cornea or crystalline lens is not spherical. The result is that light (green lines in the image) from an object may focus on the retina in one direction but not the other causing distorted vision.
To understand it simply, think of a rugby ball verses a football. An astigmatic eye curves steeper in one direction than the other – a rugby ball. A normal, spherical eye has curves that are the same in all directions – a football. If you place a cylindrical lens in front of an astigmatic eye the light will bend in one direction more than in the other. A cylindrical lens does not have the same amount of strength all over. It will be stronger in the areas where it needs to compensate for the irregular curves on the astigmatic eye. The result is that an astigmatic person can then see objects that are both in the distance and close to them clearly.