Early on when I started at TToPA, I asked one of the instructors about internal strength. He had me stand in a horse stance and told me to relax as he put his hands on my shoulders and gently pushed with one hand and pulled with the other - this caused my torso rotated to the left. He then told me he was going to do the same thing again but that this time I should resist being turned - he applied increasing pressure and I resisted without allowing my torso to be turned. He asked if I felt the twisting feeling throughout my torso and I acknowledged that I did. He explained that this was internal strength - it was clearly internal since I wasn't moving and yet there was something going on inside that was keeping me from being turned.
While this demonstration gave me my first inkling of internal strength and its connection to twisting, it certainly didn't open the flood gates of understanding about internal energy and it's application and this is a concept that I continue to struggle with.
But I got a little closer recently. I was in class - with the same instructor - and we were going over the transition from 'white crane exposes wings' to 'brush left thigh'. For this transition, you start off facing square to the east and bend a bit forward to get your arms moving and - this is the important bit - then you then simultaneously twist your torso to the right as you step out to the left - what struck me this time through was just how much internal twisting occurred in my torso as I twisted to the right and stepped out to the left - like a big rubber band being stretched from the right shoulder to my left hip and letting that rubber band snap back (albeit slowly) gave the power to transition into 'brush left thigh' - this was the first time I was able to use internal twisting to power a move and it was pretty amazing.
The other amazing thing that I noticed was that as I sunk into my left leg and continued twisting left (to face forward), the rubber band was loaded again - this time from compression from my shoulders down into my hips. When I subsequently shifted my weight from the center of my left foot to the heel (to transition into 'brush right thigh'), my foot turned out without any intention on my part - once the contact point on the foot was small enough, the compressed rubber band just pushed it open.
Having this internal rubber band loading/unloading while transitioning from posture to posture is a key part of internal martial arts but this was the first time I recognized it. I recognize it a lot more now as I go through the form - particularly with 'white crane', 'brush thigh', 'single whip', 'cloud hands', and 'part wild horses mane'. When I don't feel it in these postures, it's an indication that I've done something wrong - e.g. I haven't sunk down entirely into my foot or I've let one of my hips pop up or I've tensed up somewhere - and this helps me correct those problems. But there are still moves where I don't recognize this feeling at all - e.g. 'serpent creeps down' and 'separate thighs' - and I realize that these are moves where I have the most work to do.
Final Note: a spring may have made for a better analogy than a rubber band but a rubber band is what came to mind at the time so I'm sticking with it for now.