Core stability is more about PRESSURE than STRENGTH. In the rehab and strength & conditioning world, core stability is often trained by increasing the strength of our abdominal, oblique, and lower back muscles. This approach is missing the main piece of the puzzle: PRESSURE.
Imagine making the rubber of a tire thicker. Yes, the tire may be stronger, but what is a tire without any air?! Now imagine your abdominals, obliques, and lower back muscles are the rubber tire: you strengthened them, but you cannot create pressure within your abdomen. Your core is essentially a tire without any air. So how do we create/increase core stability?! Through creating more pressure! We generate intra-abdominal pressure through proper diaphragmatic breathing. When we take a breath, our diaphragm descends and increases the pressure within our abdomen. This increase in pressure alone stabilizes our spine. Couple this increase in pressure with the proper contraction and bracing of our abdominals, obliques, and lower back muscles, and we have greatly increased our core stability. Once we master creating pressure, THEN we can strengthen our core muscles through training.