Often a six-pack is mistakenly confused with a strong core. But in truth your core is the deeper muscles than the intercostals and obliques: Strong abdominal and back muscles are essential for doing everyday tasks, like lifting a 10kg toddler and putting away groceries, not to mention preventing an achy back and maintaining good posture at your desk, let alone a demanding sport-specific activity.  There is also a fashion for training our core, almost as a separate entity of the body.  In truth, there is little support in medical and sports research for training the core separately.  What is assured is that by working the core muscles in equal amounts with the rest of the body we will reduce injury rates, improve balance, reaction time and provide a confidence in the function of the body.

Simply - 

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The major muscles involved in the core are:

• the abdominals in the front;

• the obliques on the side; and

• the latissimus dorsi, the erector spinae and the glutes in the back.

In more detail - 

Your core extends far beyond your abs, including everything besides your arms and legs. It is incorporated in almost every movement of the human body.  These muscles can act as an isometric or dynamic stabilizer for movement, transfer force from one extremity to another, or initiate movement itself.  There are five different components of core stability: strength, endurance, flexibility, motor control, and function. If a person has greater core stability, they have a greater level of control over the position and movement of this area of their body. The body's core is frequently involved in aiding other movements of the body, such as the limbs, and it is considered that by improving core stability a person's ability to perform these other movements will also be improved i.e. core stability training will help improve someone's running ability. The body's core region is sometimes referred to as the torso or the trunk. The major muscles involved in core stability include the pelvic floor muscles, transverse abdominus, multifidus and external obliques, rectus abdominus, erector spinae, especially the longissimus thoracis, and the diaphragm. The minor muscles involved include the latissimus dorsi, gluteus maximus and trapezius.  Notably, breathing, including the action of the diaphragm, can significantly influence the posture and movement of the core; this is especially apparent in regard to extreme ranges of inhalation and exhalation.