The growing interest in robots that interact safely with humans and surroundings have prompted the need for soft structural embodiments including soft actuators. This paper explores a class of soft actuators inspired in design and construction by Pneumatic Artificial Muscles (PAMs) or McKibben Actuators. These bio-inspired actuators consist of fluid-filled elastomeric enclosures that are reinforced with fibers along a specified orientation and are in general referred to as Fiber-Reinforced Elastomeric Enclosures (FREEs). Several recent efforts have mapped the fiber configurations to instantaneous deformation, forces, and moments generated by these actuators upon pressurization with fluid. However most of the actuators, when deployed undergo large deformations and large overall motions thus necessitating the study of their large-deformation kinematics. This paper analyzes the large deformation kinematics of FREEs. A concept called configuration memory effect is proposed to explain the smart nature of these actuators. This behavior is tested with experiments and finite element modeling for a small sample of actuators. The paper also describes different possibilities and design implications of the large deformation behavior of FREEs in successful creation of soft robots.