Dietary fiber is contained in vegetables and grains. Fiber is indigestible, but still has great value. Only small amounts of fiber in the food are necessary to stimulate a process called "peristalsis" and facilitate proper digestion.
Interestingly, the grass cats like to eat doesn't contain dietary fiber. We don't know the true reason why cats eat grass. However, it's possible that grass acts like a stomach cleaner, since it helps cats spit out the hair they swallow when they're grooming themselves.