Folders store contacts in separated groups.
Categories and views are temporary forms of organization. They're useful when you want to see contacts both in subgroups and as a single collection—or when the subgroups overlap, with some contacts that fit into more than one.
Folders keep contacts really separate. For example, you might want to create separate folders for your personal contacts and your business contacts. Or you might want to keep employee contacts in their own folder separate from customer contacts.
There's one thing about folders that you should be aware of: Once you separate a group of contacts into a folder, you can't view those contacts alongside contacts in a different folder. This is what makes folders different from categories and views.