Core stability is a term that has become very popular in the world of exercise but what does it actually mean? A lot of people believe that having a good 'six pack' suggests a strong core but that muscle group is actually not part of the collection of muscles that make up your 'core'. The Transverse Abdominis; deep abdominal muscles that run from your front to your lower back, your obliques or 'love handles', your multifidius; muscles that run down either side of your lower back, your diaphragm and your pelvic floor make up the group of muscle that act like a corset around your centre, known as your 'core'. The stronger this corset can be, the more stable you can hold your lower spine and pelvis in dynamic movement. This reduces your risk of injury as you can maintain a good posture or form throughout movements like handstands and front squats and helps with the transition of power from the lower body to the upper body in movements like the clean or snatch.  Lots of movements in Crossfit help to train your core but only if you actively engage these muscle groups whilst performing the movements. If you don't ask these deep inner muscles to help during a front squat, a kettle bell swing or a press-up then an increased workload is put on the muscles of the lower spine which can put you at a high risk of injury. 

The following two articles discuss this further and suggest a few exercises to help train your core strength. 

http://www.crossfitshatter.com/blog/2015/12/21/hollow-rock-and-superman/

http://www.sportsinjuryclinic.net/rehabilitation-exercises/core-strengthening-stability/introduction-to-core-stability