Cats are obligate carnivores, meaning that they must primarily eat meat. Cats have trouble digesting vegetables and should only be on a meat-based diet.
In the wild, cats eat small animals such as mice and robins, carrion from larger animals and the odd bit of grass to medicate their digestive systems. Since cats cannot digest grass, it makes them vomit up the grass and any other bad food they have recently eaten.
Many cat kibbles are heavy on carbohydrates, which promote unhealthy weight gain. Commercial wet food is a better choice, although it can also contain toxic additives or flesh from sickly animals. The best choice for your cat is meat you choose yourself, especially organ meats such as chicken gizzards and chunks of beef heart. Organ meats contain vital nutrients that are not present in skeletal meat.