The definition of "the core" would be the region of the hips, the spine and where the center of gravity is located. Within this area we have groups of muscles which help to stabilize the spine during movement, as well as muscles which help to produce such movement. The commom misconception is that in order to work the core one must perform numerous crunches, leg lifts, cable rotations etc. But, in actuality, there is much more to working the core than strictly focusing on the muscles which everyone wants to see while they are at the beach. The deep muscles, the ones we cannot see are the most important component of the core. These muscles have been shown to be weak in people who suffer from low back pain.
It may be hard to believe, but one of the best things for the deep group of muscles is simply to maintain proper posture while performing other exercises. A push up for example, is referred to as a chest exercise, but if performed with perfect form, (which would include drawing the naval into the spine) the push up will require the core muscles to function optimally, thus serving as a great core exercise. If a push up is too challanging, try getting down on all fours and practicing drawing the naval into the spine while you are exhaling, during the inhale try to relax the abdominal region to allow for proper breathing. This will help engage the stabilizers of the core as well assist in relaxation due to the breathing patterns. From here, work to eventually perform the push up.
Another key factor in core exercises is to develop an integrated form of training them. Begin with working the stabilizers, discussed in the previous paragraph, of the core for 4 to 6 weeks. Then possibly progress to performing traditional core exercises, such as a crunch, reverse crunch or possibly even a back extension. These exercises still use the stabilizers, but now we begin to utilize some of the movers of the core. Again, these would need to be performed for 4 to 6 weeks and then another progression can be made for the core region.