From a physiological training perspective that means first, restoring the horse's natural balance and carriage when the front end is loaded with the weight of a rider, and second shifting the load more the hind end to duplicate a horse's natural carriage and movements when excited. The idea of "getting the horse to bend within a frame" is modern and backwards thinking. The appearance of the rounded "frame" comes as a side effect of the shift in balance to the rear, and is best not viewed as the primary intent. Every trainer -- and I mean every single one -- that I've ever seen put the "frame" as the goal makes the fundamental error of being in the "push-pull" school which has been taken to the extreme of its own kind of abuse in the rollkure. It really reduces the quality of the outcome significantly, even at the Olympic level.
The goal of harmony is to replicate a horse's natural balance when they are "performing" on their own, but at the request of, and under the additional weight of, the rider. Every classical movement, from the most basic to the high school level, including piaffe, passage, pirouette and all the airs above the ground, is based on horse's natural behavior and can be viewed in the pasture by the more sensitive, warmer breeds. I have a photo of my elderly arab gelding doing a beautiful canter pirouette at liberty. He also used to passage a lot. My young arab mare shows passage and potential for piaffe in pasture. I've even had a horse that did beautiful half passes in pasture, playing with me. If you watch them at play when young, you can get a really good idea of where their natural talent lies.
From an education perspective, it is about language and communication: from teaching the horse the basic aids (go forward, stop, go left, go right), through progressively increasing nuance to include forward, but not too much forward, or forward into backward (or up in the case of the above ground airs), or forward plus left or right, or forward but bend your spine into the direction of the movement.
Likewise, the aids begin as somewhat crude and visible, such as using a wide, direct rein to point the horse's head in the direction you want to go, and then as the aids are combined in increasingly more sophisticated complexes, to indirect reining. Until they become, with a really good pairing of horse and trainer, totally invisible to the outside eye.
Horse's can feel a mosquito walk on their body. There is no need to see riders hands and/or legs moving at all. They can feel every bit of a rider's muscle tension and, properly handled, can appear to be doing dressage under a rider on their own or feel like they are responding to your thoughts because even as you think what you are going to do, you're body begins to prepare for the aid, which they feel and respond to.
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