The "core" is the body area around your trunk and pelvis, and core muscles are those in your back, abdomen, sides, pelvis, and buttocks. Strong core muscles help protect your back, stabilize your center of gravity, and keep you balanced so that you can avoid falls. If your core muscles are strong, you can easily bend to pick something up and stretch to reach items on a high shelf. Strong core muscles are also essential to good posture and a pain- and injury-free back. If your belly looks and feels flabby, the underlying core muscles are probably not in good shape, regardless of your weight. They can be weakened by neglect and a habit of slouching. They also get stretched out during pregnancy; to get them back in shape, women have to exercise during pregnancy and after delivery.
Various types of exercise can help you strengthen your core. One option is the Pilates Method, a popular and intense form of strength training based on the idea that the abdominal and pelvic muscles are the body's power center. Unlike weight training, it does not attempt to develop individual muscles. Pilates is done with an instructor or at a health club, using special machines or rolled-up towels for floor exercises. Movements are slow and aim to engage the mind as well as the body. Traditional Pilates isn't recommended for older women at risk for osteoporosis, since repeated, forceful flexing of the spine (forward bending) can lead to vertebral fractures, and eventually even to a "dowager's hump." (Here's more on the relationship between Pilates and osteoporosis.)
Another option is tai chi, a gentle form of movement, perfect for those with osteoarthritis or other musculoskeletal impairments. It can build core strength and musculature of the lower limbs, as well as improve posture, balance, flexibility, and mobility. Tai chi can also facilitate relaxation and focus even while executing the moves. And it synchronizes the musculoskeletal and nervous systems, helping to develop concentration and coordination and so reducing risk of falls.
Yoga can help, too, by improving muscle tone, flexibility, balance and stability.
In addition, there are many traditional exercises that you can do at home or at the gym to strengthen your core. These include crunches (abdominal exercises), pelvic tilts, squats, and lunges, as well as exercises for the upper body. Some exercises for core muscles involve the use of a stability ball – a large inflated ball you can rest your body on. These aren't as easy to use as they look, so it is best to get some instruction. If you're not accustomed to working out, I suggest scheduling a few sessions with a personal trainer who can assess your level of fitness and teach you how to perform the exercises properly.
Andrew Weil, M.D.