There's now plenty of resources on this, as it becomes more recognised. You may have more success if you look up the Scales of Training, rather than the European Training Pyramid.
Rhythm > relaxation > contact > impulsion > straightness > collection. This is the general structure of the scales, but rhythm and relaxation are somewhat interchangeable, as are straightness and impulsion.
Rhythm: This is the first step. It refers to the horse's movement and balance, which should be in a nice rhythm regardless of pace. So for example, a walk is a four beat pace. The timing between the beats should be even, like a drum beat. Many young horses, or unschooled horse lack a rhythm and often put in a hurried or slow step. Lame horses are an extreme example of how a lack of rhythm sounds/feels. So say the full stops are pause lengths, a walk should be: 1...2...3...4 but it's often: 1.....2.3...4
Relaxation: A horse with tension will not progress further in the scales. At least, not properly. It's possible to be strong but relaxed, similar to how we are as riders. The horse should be willing and happy. The reason this step and the last are interchangeable is because horses sometimes do not become relaxed until they become balanced, others do not become balanced and form a rhythm until they relax.
Contact: Contact does not mean hauling on your horses mouth and forcing him/her into a false outline. Here, contact means acceptance of the aids. The horse should chance pace, stop, turn, and so on when told to (via reins or seat etc.), whilst keeping the rhythm and relaxation achieved from before.
Impulsion: Impulsion means that the horse's energy and power is coming up from behind, through the back and into the hands. It's using those big hindquarters to propel itself upwards and forwards, as opposed to dragging itself along by the forelimbs, which majority of horses do.
Straightness: Straightness means the hind feet follow the front feet. Straightness doesn't apply just in a line, but also in a circle. Again, this is interchangeable with impulsion. Some horses cannot go straight without the power coming up from behind, where as others cannot properly utilise their energy unless they're going straight.
Collection: The end game. What most people work towards, and many take shortcuts to get to, and create false outlines. Collection, true collection, happens when everything else is in place. The horse's weight is transferred mostly to the hindquarters, and those hindquarters act like springs. The back is strong and weight carrying (one of the biggest indicators of a false outline is a hollow back). Basically, the horse is using itself well.
The scales take time. How much time depends on the horse and its current level of training. There are plenty of exercises to achieve each step. It can take months, if not years to go from the first step to the final step. It's not really something that can be achieved overnight.