Neal,
My response was based on the assumption that what you wanted to do was to back up (create a duplicate copy of) all of your iTunes files (music and library), to protect against the possibility of failure of your internal hard drive, software corruption, etc. Some of the other responses addressed a different goal, re-locating your iTunes music and library to the external drive (so that iTunes would actually play each selection from the external drive). Let us know which of these alternatives you are trying to accomplish.
Also, note that my instructions were to copy the folder called "iTunes," which is a top-level folder within "My Music," not "iTunes Music," which is a sub-folder of "iTunes." By copying the top-level iTunes folder you would be simultaneously backing up both the library files and the music.
As was noted by one of the others, the library files contain information about the music, which among other things is used to provide the entries (name, artist, composer, etc.) that you see in the listings that appear when you open the iTunes program.
Regards,
-- Al