Anti-war Democrats became known as Copperheads during the Civil War. They opposed the war which they blamed on abolitionist and supported those who resisted the draft. Many of the Copperhead offered encouragement to Union soldiers leaving the war, trying to increase the rate of desertion. There was even some talk about releasing Confederate prisoners of war.
The Democratic Party broke along regional lines during the 1860 Presidential race, which allowed Abraham Lincoln the Republican candidate to become president. As secession became a reality, Northern Democrats felt more conciliatory toward the Southern state then the Republican did, and they began calling themselves Peace Democrats. A large portion of these Peace Democrats were located in the Midwest, and it was during the Indiana Democratic Convention that the Cincinnati Gazette coined the named Copperheads for this group on July 30th 1862. The name came from the copper pennies many wore as badges.
Copperhead reached their height at the 1864 Presidential Convention when one of their leaders Clement Laird Valladigham of Ohio persuaded the party to adopt a platform which included calling the war a failure. When the war ended so did any backing the Copperheads had enjoyed. Most in the north felt that the Copperheads had actually made the war longer, by holding out hope to the Confederate states that northerners wanted peace.
If you would like to read more, check out the web site, Illinois Copperheads and the Civil War