A common assumption in problems of rotation, angular momentum, and torque, and one commonly encountered in reality. A rotating object, usually circular, rolls against another object (very often a flat surface) without any slipping between the rim of the object and the object or surface it is rolling against. If the rotating object is a disc and the surface is a flat one, then the speed of the center of the disc relative to the surface is simply the speed of the edge of the disc.
A tire is usually constrained to roll without slipping by the frictional force between the tire and the road. A rack and pinion system is constrained to roll without slipping by the teeth of the gears. Similarly, two gears will roll against each other without slipping because of their meshing teeth.
Rolling with slipping may occur if nothing constrains the surface of the rolling object to stay in close contact with the other surface. A wheel in a mudhole, or two cams with oil on the surface between them may more easily roll with slippge, for imstance.