Vegetables and cheese are grated so that they are very thin; much thinner than can be achieved with a knife. Grated cheese is used in sandwiches and salads and hard cheeses such as parmesan are very finely grated to sprinkle over Italian dishes such as spaghetti bolognese.
Graters come with different size holes. The larger the holes, the larger the pieces that are cut. If a recipe asks for finely grated, use the smaller holes on a grater.
Be very careful to keep your fingers and knuckles away from the grater. It’s not great to grate your fingers!