Directory and Subfolder are the same thing. You shouldn't be dumping all of your .html, .jpg, and .gif files in the same directory. However you created the website on your home computer is how it should be transferred over. If you built it in, say, a directory called "web," you need to do this for FTP:
FTP to the server and change into the domain.com folder. For your local directory, change into the "web" folder. Now select all and drag everything over: all files, all folders, all at the same time.