Cats like to eat grass - Photo by Irregular Shed (Flickr)
Pica in cats means eating non-nutritional objects. Pica can affect any animal including the human animal. It affects dogs more that cats1. The condition's name comes from the Latin word for magpie, a bird which is reputed to eat almost anything1.
In the cat world, pica most often manifests itself in eating plants or fabrics. It could be argued that a cat eating plants is not strictly pica as wildcats eat vegetation and some more than others - see The cat that eats vegetation. Cats also eat grass for the folic acid in it.
For full-time indoor cats, eating plants may well be the only available substitute for eating grass. However, some plants are poisonous to cats - see also: House plants poisonous to cats. Cat keepers should only keep non-toxic plants.
It is thought that wool chewing and sucking is due to early weaning. More research is required. Another theory is that it happens because the cat needs to ingest indigestible fibre. Once again this has not been firmly established.
Perhaps the more likely theory is that it is a form of OCD - obsessive compulsive disorder. OCD can also be manifest in over-grooming and tail biting. Feline endocrine alopecia can in fact be OCD over-grooming. See also: Maine Coon hair loss and Hair loss in cats.
OCD may be due to stress. Discovering the underlying cause of stress in your cat and removing it must help. Drugs can help too but these are a definite last resort in my opinion. All drugs are poisons, ultimately. Sometimes increasing the number of meals a day can also assist. Finally, allowing your cat to eat grass would no doubt assist in reducing plant eating.
1. Wikipedia authors
2. The Cat, Its Behavior, Nutrition & Health by Linda P Case - page 180 - Neville PF and Bradshaw JWS, Unusual appetites.