Cataract surgery involves replacing the cloudy natural lens in your eye with a clear, intraocular lens or IOL. These IOLs correct myopia, hyperopia, but not astigmatism.
To simplify, eyes without Astigmatism have a round shape and a fixed focussing power over its surface. Eyes with Astigmatism have an oval shape and variable power.
Conventional IOLs do not correct astigmatism. With the advancement in intraocular lens design, patients can now elect to have the astigmatism correct during a cataract surgery with the insertion of a toric IOL.
These specially designed lenses neutralise the eye's astigmatism. The procedure to insert the toric IOL is the same as conventional cataract surgery where the artificial lens replaces the natural cloudy crystalline lens.