Cats do need to eat grass. If they didn't have access to grass, they eat any other plant they can find, including flowers. They do that to clean their digestion system from inedible parts(1), as for a home cat, that's mostly their own furballs.
"Cats regurgitate when they eat grass because they lack the necessary enzymes to break down vegetable matter. Does this mean your cat likes to throw up? Well, while it's doubtful that kitty enjoys the act, this up-chucking sensation may eliminate all indigestible matter from the cat's digestive tract, making it feel a whole lot better. This is important because cats eat their prey as is, including both the edible and inedible parts (fur, bones, feathers, etc.)"