Note: Parmesan is never vegetarian, it always includes calf's rennet which is a meat product. If you're a strict vegetarian or if you're cooking for a strict vegetarian you need to substitute a different type of cheese of look for a different recipe. See Cheeses that aren't vegetarian for more.
About Parmesan[]
Parmigiano-Reggiano (IPA: [ˌparmiˈdʒano reˈddʒano]) or Parmesan, is a hard granular cheese, cooked but not pressed, named after the producing areas near Parma, Reggio Emilia, Modena, and Bologna (all in Emilia-Romagna), and Mantova (in Lombardia), Italy. It is made from raw cow's milk.
Grated Parmesan[]
Many stores sell a product labelled as "grated parmesan", but this is not always actually Parmesan cheese, it often contains whey and other milk solids as filler. The best grated Parmesan is freshly grated cheese.