An abdominal six-pack will look good but does not in any way signify that you have a strong core. It does give you an outer layer of your abdominal musculature, but this has nothing to do with the core.
Your core muscles are the group of muscles that act to stabilize and control the spine and pelvis, and this is what influences the upper body and legs. When you talk of developing core strength you are not talking about power but of the ability of your body to maintain an ideal posture that promotes the ease of movement and places less stress on the joints. This core strength will allow you to easily get on and off the floor, stand up from a sitting position, sit comfortably while working at a desk, and carry out any physical activity or chore without pain. Athletes benefit from strong cores by having movements that are efficient and thus improve performance while reducing the chances of injury. Strong cores prevent injuries from overuse of muscles, make the body resilient and allow the body to bounce back easily during rehabilitation from injuries.
Pelvic musculature is part of the core and any weakness here can lead to problems with incontinence. Age can lead to degenerative changes in the spine. Bones and cartilages are prone to wear and tear, and these symptoms can be controlled and even eliminated with the right core exercises. When your muscles which help in posture are strong and stable they help in the suspension of bones and other structures, and this allows for ease in movement.
You can even control rotation and curving of the spine, scoliosis, with the right exercise that helps in posture. When your core is not strong and is imbalanced, it will result in problems all over the body. Insufficient stabilization of the pelvic muscles can lead to pain in the knees. Runners will develop back and neck pain while indulging in their sport because the muscles in their core which act as shock absorbers are not working as they should.
A good program for developing core strength is not just the repetition of exercises, but being aware of the muscles that need to be activated to accomplish this task. You have to concentrate if you want to activate your core so that you are properly tuned to the needs of your body. There is no one way of strengthening the core of your body, and while some may do well with Pilates or Yoga, others may not. It is best to take the advice of physical therapists to understand the method that works for your body in strengthening its core.
Be patient while you find your core, and once you have done so, and understood the bunch of muscles that are the core, see that you exercise them in every action, whether you are running, walking, sitting or even driving. The daily practice of core movement can lead to movement patterns that are not only healthy but will increase your mobility throughout your life.