You can easily organize your PDFs in ReadCube Papers by creating Lists.
To create a list click on the gear icon next to All Papers.
Then simply name your List (you can also select if it needs to be nested into another list) and then drag and drop your PDFs.
Lists in ReadCube Papers behave like playlists, rather than folders. An article can exist in more than one list at a time. For instance, if you have a list of articles about cancer and another list of articles about mitosis, you can file the article "Mad2 over expression promotes aneuploidy and tumorigenesis in mice" in both lists, since it is relevant to both cancer and mitosis.
If you delete a list in ReadCube Papers, the PDFs in that list will not be deleted. They will remain in your library.