Folders in Zotero are referred to as Collections. You can also created sub-collections within a collection. Unless a specific collection is selected, Zotero places items that are being imported into a new collection.
Zotero can store pdfs of items to allow you easy access.
When you have a pdf (from a database, from interlibrary loan, from a colleague…), it can easily be added to your Zotero Library.