I haven't taken many lessons, nor had any "eureka" moments during them. Actually, they've mostly been pretty disappointing.
I can attest to the plateau, breakthrough, rapid improvement, plateau, breakthrough cycle though.
The first one was probably my first carve, back in the bad old days of straight skis. I was going way too fast, needed to change direction, and it just... worked...
Other breakthroughs have been because of various things: Imitating racers and freestylers, improved equipment, focussing on improving various elements, ie. hand position, pole plants, upper body "quietness," looking in the right place, "centeredness" and balance... And all of the technique things seem to involve "doing less" with muscles and more with the skeleton, which makes sense biomechanically...
Chasing skiers who are much better than me also seems to drive the breakthroughs, unfortunately you don't get time to think about what you just did until you get to the chair.
I may need another lesson soon though: Last year I made some major improvements and got a lot smoother, but I'm starting to plateau again and I'm running out of ideas on things I can change. I should probably join a race league or something -- I probably need a "coach" more than an "instructor."