Contrary to popular belief, when pets, like cats and dogs, nibble on grass it does not necessarily indicate that they are sick. Veterinarians believe that these domesticated animals have become more omnivorous than carnivorous in their time as pets, and grazing on grass is simply a manifestation of their omnivore status.
Additionally, eating behaviors for both cats and dogs are influenced by their mothers' diets before waning. Veterinarians believe that eating grass acts as a digestive aid for cats who might need a little extra fiber in their body. Since fiber is not digestible, it adds bulk and the diet and could be a natural treatment for a little bit of feline indigestion. However, veterinarians are still unsure as to whether this also applies to dogs, but it is usually assumed that dogs eat grass for the same reason.
All that being said, eating grass does not necessarily mean that Fido is sick. Just like humans, pets can fall victim to the "monotony effect," becoming bored with their regular diet. Although grass may not seem so appealing, cats and dogs appreciate it as something different that kibble.