The "core" is a loose term thrown around the health and fitness industry, especially when it comes to "core training". There is a lack of consistency when people discuss the term "core stability", however an article by Tricia Majewski-Schrage, Todd A. Evans, and Brian Ragan in 2014 helped to develop a consensus amongst content experts of a working definition. "Core stability is the ability to achieve and sustain control of the trunk region at rest and during precise movement". The authors also agreed that essential components to core stability included muscles and neuromuscular control. We like to think of the core as a force transducer within the kinetic chain; a medium for transferring energy and force from the lower to the upper body. Think of popular sports and movements like pitching in baseball, or a golf swing.
The content experts all mentioned 5 key muscles to core stability: the transversus abdominis, internal and external oblique, rectus abdominis, and multifidus. It is important to note these muscles connect to the pelvis, the spine, or the ribcage. However it is important to appreciate muscles of the lower and upper body that AFFECT these core muscles. For instance the glutes connect the femur (long leg bone) to the pelvis. The serratus anterior connects the scapula to the ribcage. If there is an underlying dysfunction of these muscles, core stability can be AFFECTED due to the overlying fascial connections. Therefore the core stabilizing muscles mentioned earlier may not be able to stabilize the trunk, keeping it stiff and still.
Here is one of my favorite warm-up routines described in an article by Benjamin C Y Lee and Stuart M McGill to activate the core stabilizers and increase stiffness.
1) Side planks with banded clams
2) Banded Single Leg Bridges
3) Alternating isometrics of obliques and abs at 90/90
4) Banded bird dogs
5) Modified buttress presses
Do 5 sets of 5 reps of each exercise before any exercise or activity, and you'll feel more in tune with your body because your nervous system and appropriate muscles have been woken up!