Moving a weight through gravity while standing in an upright position challenges a number of muscles to work together to generate the forces that create and control those movements; this is one of the greatest benefits of using a medicine ball for core strength training. You can use a medicine ball to perform pushing and pulling movement for upper-body muscles, rotational movements where your hips and shoulders counterrotate to involve a majority of your core muscles, and hinging, squatting, and lunging movements to strengthen lower-body muscles.
Try these medicine ball exercises for core strength from Smarter Workouts.