When someone mentions training the core, one of the first thing that pops into most peoples heads is getting that six-pack ready for beach season. However the "core" serves a much greater purpose than simply aesthetics. The musculature of this area of our body includes the muscles of the abdominal wall, the back extensors, the quadratus lumborum, as well as the psoas and gluteals. These muscles function much differently than the muscles of the limbs so they need to be trained differently as well.
A common misconception is that performing repeated flexion of the trunk is an effective way to strengthen the core. A good core strengthening program includes movement through all 3 planes of motion as well as anti-rotational and stability exercises as the core's most significant functions are its ability to brace, stabilize, and assist in balance. Core stability is essential in maximizing force generation and minimizing joint loads in activities ranging from running to throwing.
Many studies have shown that strengthening the core is a good way to prevent injury. One of the most common chronic injuries is Low Back Pain, which is often caused by poor muscle endurance, muscle imbalances, and muscle inflexibility in that area. A 2010 article in the Strength and Conditioning Journal documents that training the flexors, lateral musculature, and extensors of the core for an extended period of time can prevent any new back pain incidents and helped to control existing pain.
Bottom line, core strengthening is essential for improving athletic performance and preventing injury.... looking good is just a side effect.