A gun which is not rifled and whose barrel is completely 'smooth' all the way from breech to muzzle. The projectile is not spin-stabilised and hence the guns are relatively inaccurate. The most common modern gun that is a smoothbore is a shotgun.
A gun is smoothbore if the inside of the barrel is completely smooth. Smoothbore guns were used before rifled guns were developed. Although smoothbores were not as accurate and had a shorter range than rifled arms, there were still plenty of them in use during the Civil War.