Sheep often get cuts and scratches from the things around them.
Parasites attach themselves and infection soon follows.
The oil was the little flask of medicine the shepherd always carried to soothe and heal. At night, as the shepherd gathered his sheep into the fold, he would check each of them individually for any sort of cut or wound. As he lovingly and gently felt of the sheep he would apply, ever so carefully, the oil of healing. The oil softened the wound, eased the pain, and the shepherd's touch reassured the sheep of his complete care. The care of the shepherd was so complete, that he not only led the sheep beside quiet waters but would smooth out a place so that the water could flow from the deeper streams into a shallow depression in the ground.