The action which forced me to understand core strength is the spin.
Core strength is the ability to stabilize the pelvis and lower spine. The abs and the pelvic mucscles are used to establish that stability.
When I first started dancing, I couldn't do a spin to save my life. Finally, I met another amateur who told me that it's very important to keep tone in the muscles that I mentioned to tighten up the motion.
What I noticed was the fact that tightening the hips and abs makes it much easier to maintain the correct posture through the upper body - the very essence of a good frame.
The only trouble that I have now with spins is getting my new partner to do them correctly.

jj