A smooth bore weapon is a firearm which lacks rifling inside the barrel. This can be either small arms ranging from the earliest hand cannon to a state of the art modern shotgun or ordnance from a primitive bombard to a cutting edge tank cannon. Almost all mortars are smooth bore.
All firearms prior to the invention of rifling were smooth bore, and whilst muzzle loading weapons were the norm, smooth bore could continue to justify itself as it allowed a higher rate of fire than could be achieved by a rifled weapon1. However smooth-bore weapons tend to be less accurate as the rounds that they fire are not spin-stabilised like those from a rifled weapons, and with the normalisation of breech loading they have been supplanted by rifled weapons for most purposes.
As of the 21st century, the uses of unrifled weapons tend to be limited to the firing of loads for which accuracy is not important (such as flares), or where rifling would not be effective (such as the multiple shot shells of a shotgun) or would be actively unhelpful (as in a modern tank gun).
In some cases the ammunition fired by a modern smooth bore is self stabilised - for exampe the long-rod penetrators fired from modern tank guns are fin-stabilised, as are mortar bombs and some shotgun slugs are designed with a driving band that mimics the effects of rifling.