There is no option to make a copy of your original files after you import the file references into the LR catalog. (During the import, a copy could have been made.)
Copying the originals (making a backup) needs to be done outside of LR, either using tools from your OS or other third-party tools.
The easiest approach would be to copy the root directory of your photos directory tree to the external drive. The original files will remain on the hard drive where they are now and LR will still reference them on the HD, no keywords lost.
I want to back up my photos on another hard drive and access them from my main catalog? How do I do that? If I use Lightroom to move the folder onto another hard drive it does not give me the option to copy them. I have to actually move them, which defeats the purpose because I still have only one copy.
All of my images are in DNG format.
You make backups using a dedicated and automatic third-party program. This eliminates the possibility that you will forget (or be too lazy) to perform regular backups. This makes it easy to have backups every single night, and thus you can never lose more than one day of photos. I use WinZip Pro but there are dozens of such programs available.
You also need to (this is mandatory) make regular and automated backups of your catalog file. Your keywords are in there. If you don't make backups of your catalog file, you could possibly lose all of your keywords and all of your edits. You can (and should) do this automatically from within Lightroom.
I want to back up my photos on another hard drive and access them from my main catalog?
Backup copies should never be accessed by LR or any other editing application. They are "safety net" copies to be used only when the original image files become lost, damaged, or corrupted.
As dj_paige explained you also need to include regular backup copies of your LR catalog(s) on the backup hard drive. Any file & folder backup application will do this for you by keeping the files and folders on your backup drive up-to-date (i.e. synchronized) with the primary drive. If on a Mac you can use Time Machine if on a Windows system there are numerous applications available, both paid and freeware. I use FreeFileSync for backing up all my media files, including Pictures, Music, Videos, Documents, Settings, and of course LR catalog.
If you're intention was to use the backup copies as separate editing copies, please take a look at Virtual Copies.