to keep your back strong
Core exercises keep the muscles around your trunk and pelvis in good shape and help to prevent back injuries.  Core exercises improve your balance and stability.  Training muscles in your pelvis, lower back, hips and abdomen help your body to work in sync.  Running like many other sports depends on stable core muscles.

Core exercises do not always require specialized equipment or a gym membership.  Any exercise that involves the use of your abdominal and back muscles in coordinated fashion counts as a core exercise.  The video above shows just a few, quick core exercises you can do at home.