Correct, Jane, there is nothing 'magic' about web sites and 'servers'. The 'server' connects your folders to the domain name you tell the hosting company to use. It's like a password that gets you into your own set of folders on your drive. Once you have that 'main' folder, you just create new folders inside it and even folders inside those, if you want. A "URL" is simply a way of telling the server what path to take to access whatever is the last item in that URL. Almost exactly what you are telling the OS when saving or selecting a file in those navigation windows, the OS just provides a different way of doing it. But you can actually see that whole 'path' by using command F and selecting one of the items found. At the bottom of the window is the exact 'path' to that item. Or, open some folder deep inside your drive. Now, command-click the folder icon and you'll get a list of the other folders that one is in, all the way back to your hard drive itself.
Not sure what Cyberduck does any differently than any other FTP program, but they all should have a way of looking at your file/folder structure similar to what you see in a Finder window. Your space on the hosts server is just another series of folders that you can create, name, delete, rearrange, set/changes permissions, etc. No 'magic' involved, the instructors should have covered this in the first or second lesson, IMHO.