"Copperhead" was a term given to people in the north who sympathized with the south during the Civil War. They were also called Peace Democrats; they were openly critical of Lincoln and called for a speedy end to the war.
It's Bill Creighton who is considered to be a Copperhead. His brother and cousins and most other young men have joined the US Army, but Bill decides to fight for the Confederacy. This causes not only external conflict with their neighbors but also internal conflict, since a son is fighting for each side in the war.