Good grief. I have worked so hard at understanding this and teaching my horse with the help of my trainer, it is hard to explain period, let alone on a forum. I can tell you the things that helped me and my mare start to learn it.
The first step was getting her to understand vertical flexion, or giving at the poll. Teaching them requires an immediate release initailly when they give you the correct response. Then you can hold it longer and longer. We did that at a halt and also backing initally. Then to start getting her under herself, we trotted (my trainer says it is easier physically for them to learn at the trot rather than the walk) in small circles, with me sitting back driving hard while asking for that flexion at the poll.
As soon as she would give her head, I would release. Just as the original teaching of vertical flexion, I would hold the position longer and longer. She learned quickly. Now I just gently collect my reins, sit back and drive her foreward and she will push her hiney under her and flex at the poll. We can do it at the trot and walk, but are still working on canter. When you get it right it feels so -awesome-!
I am so proud of us, collection has been a goal of mine for a long time even though I'm mostly a trail rider and I finally feel like I am starting to get it. People sometimes do not understand this, but the ability to collect helps everything. Even going down hills on trails, sometimes all the other horses are rushing, and my mare wants to rush, and I get to say, " Uh uh! We are going to collect a bit." Then she gets her butt under her, softens to the bit, and goes down in complete control. It is well worth the work
An analogy I have heard to understand collection is to think of the horse like a bow (as in bow and arrow). You want the horse to come up under you like a flexing bow, you drive the energy from behind and capture it up front to hold the bow flexed under you.