Before email, a carbon copy was a copy of a document made by sticking a piece of carbon paper between two blank sheets. Then, when the document was made on the top sheet, an exact duplicate would be made on the bottom. Before the advent of photocopying (xeroxing), a carbon copy was the only practical way to make a copy of a document.
According to my dad, one of the worst feelings in the world is when you've spent two or three hours typing up an eight-page report and you suddenly realize that you've been putting the carbon paper in backwards. So instead of making an extra copy of your report, you've just created a mirror image of the report on your originals.