Astigmatism is a condition in which the cornea is curved more in one direction than the other causing the cornea to resemble an egg or football shape rather than being round like a basketball. Astigmatism causes blurred vision at all distances, as shown in this picture.
The eye functions by focusing images i.e. the stop sign on the left in the picture. There are two ocular structures that achieve this focusing, the cornea (or the clear window of the eye) and the natural lens (much like the lens in a camera).
Together they focus or compress the parallel light rays onto the retina (back structure of the eye, much like the film in a camera). The image is displayed on the retina and a photochemical reaction occurs. The image is then transmitted through the optic nerve to the brain where we actually see and interpret the image as clear or blurry.
With astigmatism, the cornea is curved and the image strikes either in front or behind the retinal at different perpendicular plains resulting in distortion of the vision. This is represented in the picture by the stop sign in the middle. Since it misses the retina, the image you see is blurred (the stop sign on the right).