Continuous insulation—typically provided by rigid foam board applied to the exterior—increases the thermal performance of a framed wall in two ways. First, rigid foam provides more insulating value per inch than cavity-fill insulations, so it's the easiest and most cost-effective way to add R-value to a wall with the least increase in wall thickness. Second, continuous insulation (applied over the structural sheathing or directly to the exterior face of wall framing) eliminates much of the thermal bridging—the conduction of heat through studs and headers—that robs most framed walls of energy.
There are three types of foam that can be used as continuous insulation on the exterior of the building.