The cornea (the front clear window of the eye) is normally more curved in one axis, like a rugby ball, so that light focuses unevenly on the retina and cannot be focussed clearly by a spherical (round) lens. This is called corneal astigmatism.
Astigmatism commonly occurs along with myopia or hypermetropia. A small degree of astigmatism is very common and has only a small effect on the vision. Higher degrees cause a greater degree of blur and distortion of vision and require a complex “toric” corrective lens that is more curved in one axis. The component of the lens that is required to correct astigmatism is shaped like a cylinder. If you have astigmatism, your spectacle prescription might therefore read “cyl +1.50 axis 180” to indicate that the focus power of the eye needs to be adjusted by a lens of one and a half diopters strength aligned with the 180 degree axis in order to see clearly.
Astigmatism can reduced at the time of lens surgery either by changing the curvature of the cornea using incisions placed to relax it where it is steeper or by compensating for the astigmatism using a specially made “toric” implant lens that must be orientated correctly inside the eye.