Plug in your external hard drive. It should auto mount and place an icon for it on your desktop. Hit Command + N, a new window will pop up. Find the location of your photos in that window. Click (and hold down) on the folder your photos are in and drag it to the icon of your external drive. That should only copy the photo folder to the external drive.
After it finishes, open up the external hard drive with the icon on your desktop and verify that all of your photos copied over. After you verified your photos are all there, click on (and hold down) your first photo directory and drag it to the Trash. Then empty the Trash, you should be good after that.
Good luck. 🙂