Core stability is very important not only for athletic performance but also for injury prevention. Research studies have shown a link between lower extremity injury and poor core/postural stability. Core muscles are the ones that attache to the pelvis, which include abdominal muscles, hip muscles, back muscles, etc. Each muscle play an important role in providing stability, however, the muscle called transverse abdominis seem to be very important when it comes to core stability. What this muscle does is that it compresses the trunk working almost like a girdle when it contracts. When doing core exercises, this muscle should be focused on not just other '6 pack muscel' and the ones that make you look better.
1) Draw-in
The easiest way to work this muscle is to do draw-in exercise. Sometimes, it is called pelvic tilt or ab set or iso abs. This is done by laying on the back with knees bent at around 90 degrees and trying to draw the belly button in towards the back. Or you can try to make the back flat against a table or floor. Sometimes, it is easier to do when you have a hand of someone's between the lower back and floor and try to press the hand down. You should not hold your breath or other body areas like neck and arms should be relaxed. Try to hold this position for 10 seconds and repeat 10 times to start. It may not as easy as it looks to do this exercise the right way.