The cornea is the clear front layer on the surface of the eye that does most of the work of bending light as it enters the eye. Light must be bent properly so that it creates a sharp image. Theoretically, the eye's cornea should be perfectly round, like a slice off the surface of a ping-pong ball.
When parallel light rays pass through the cornea, they should be bent just enough to meet and focus on the retina (the light-sensitive membrane that lines the back of the eye). The lens is responsible for fine adjustments of focus.
Astigmatism is a condition in which the cornea is oval, like the bottom of a dessert spoon. This means that the light rays focus at different points in the eye. As a result, the focus is smeared so that while lines in one direction may be sharp, lines in another direction will be blurry.