An astigmatism is when your eyes cornea is curved in an egg shaped instead of symmetrical like a ball. With this condition the light comes in at two different places which results in vision that is blurred or distorted. Up until recently people with an astigmatism could not wear contact lenses but toric contact lenses allow even people with an astigmatism to be able to see without glasses.
The toric lens is actually made from the same material that traditional contact lenses are made from but the lens is designed differently to deal with the astigmatism. These lenses curve at different angles creating two powers. In addition they also have a way of keeping stable when you move your eye or blank so that they provide crisp clear vision.
While it will take your eye doctor longer to fit you with the toric contact lens, you'll be happy to know that they are available in disposable, multifocal and even colored. Be that as it may, you can expect to pay more both for your lenses and for the fitting. Fitting an eye with these lenses does take a certain amount of expertise so you might want to make sure that your eye care practitioner is experienced with these types of lenses.
You can get toric lenses in soft or rigid gas permeable. With this type of lens, some people actually like the rigidity of the RGP lenses because they provide a bit crisper vision which is important with an astigmatism.
Many of the manufacturers today make soft toric contact lenses and your eye doctor will be able to recommend a brand that is best for your eyes. You can get them as disposables, daily disposables frequent replacement and silicone hydrogel for 30 day wear. If you have presbyopia, you'll want multifocall tprics which are typically an RGP lens and not disposable although there are some manufacturers who do make a soft toric multifocal lens.