Items in Zotero libraries can be organized with collections and tags.
“Collections” allow hierarchical organization of groups of items, in advance of adding items to your library. Item may be placed in multiple locations (sub-collections) in your library collection. Items may then be retrieved by “drilling down” into the hierarchy.
It is important to understand that items can be assigned to multiple collections, and that doing so does not duplicate the item. In this sense collections are more like iTunes playlists than folders in a computer filesystem: just as a single song can be added to more than one playlist, a single item in a Zotero library can be added to multiple collections. The library root—“My Library” for personal libraries or the group name for group libraries—always shows all items in the library, and items are duplicates only if they appear multiple times in that view.
“Tags” (also called “keywords” in other contexts) allow for detailed characterization of an item, and have the unique advantage of allowing the formation of ad-hoc collections after adding items to your library (e.g., one can use tags to locate items tagged “Sumarian” + “history”, and so on.)
Both organizational schemas have unique advantages. Experiment with both to see what works best for your own workflow.