Core training has gained a lot of popularity in recent years. Training your core muscle group is more involved than training just your abdominal muscles. Your abdominal muscles are comprised of just a couple of muscles that have somewhat limited functions. The core muscle group is larger and has more important function.
The core muscle group surrounds your torso and is responsible for helping to stabilize your pelvis and spine. Together, these muscles are what allow you to stand upright and walk on two feet. Improving the conditioning of your core will give you a greater range of motion in your torso and, more importantly, give you more stability and strength around your spine. Poor core conditioning will result in poor mobility and stability.