Rolling may be seen in numerous contexts and describes a behaviour where the cat assumes a posture of dorsal recumbency (i.e. it lies on its back) with all four paws held off the ground. The body is moved laterally (swinging from side to side so that the left and right sides are alternately contacting the ground) and may also be curved backwards and forwards synchronous with or in opposition to the lateral movement. For example the body weight is shifted towards the cat’s left and the left fore and hind limbs are brought towards one another through lateral flexion of the spine. Alternatively the cat’s body weight may be shifted to the cat’s right, but the hindquarters may be swung towards the left and the forequarters towards the right (and other permutations of such movements). When rolling the tail may be still, the tip may twitch or it may lash. Facial expression, head posture, vocalisations, degree of limb extension or flexion and whether the claws are extruded or sheathed will depend on the motivation underlying the rolling behaviour.
This video demonstrates rolling.