A horse's "motor" is in the back - his impulsion, the energy that drives him forward, comes from his hind end. If he is placed in a position where his weight is rocked back, his spine is arched upward, and his hindquarters are well under him, he is in the best possible position to produce that energy because his body is properly aligned. Just as (if you are a dancer), you rise slightly on your toes and lift your head, shoulders and solar plexus before you step out.
Now, you have your horse with his forehand lifted, his spine arched upward, his hindquarters tucked under, and he's ready to step forward. As his hind legs push him forward, the way his spine is aligned will direct the momentum from his hind legs - THAT's what I'm calling "energy" - the horse's momentum that takes him where he wants to go.
With your legs and your hands, you DIRECT that energy - the "push" moves the horse straight forward, to one side or the other, or around a curve. Your leg aids generate the "push" and then direct it. When you place the horse on a bend and move him forward in a bend, your legs are doing two things at once: you're giving him the aid to move forward - to "push" - and at the same time your legs shape his spine to determine the direction the "push" is going to go.
Now for the part that's hard for Western riders because you don't ride "on contact": by riding a horse with a "feel" of his mouth (and you can't do this in a Western curb - you have to use a snaffle or a combination bit like a Pelham or a double bridle) you can contain or hold back the "push" or energy for some period of time. Your legs generate the energy in the horse's hindquarters, he pushes forward, but your hands by holding contact (maybe slightly firmer as you push) tell him "don't go freely forward." All that energy has to go somewhere, so it goes UP - the horse arches his back and neck and lifts his forehand.
Now, if you pull too hard or push too hard, the whole edifice will collapse - the contact can't be static, it has to go somewhere. (That's why a horse will rear if you pull too hard on the reins while pushing. You're telling him GO! but DON'T GO FORWARD! So he goes UP.) You have to allow the horse to move forward on the bit, dispelling some of the energy in forward motion, while the rest of the energy is still going into the lift of his forehand.
What I'm talking about with the energy on the bend is that the outside rein doesn't allow the horse to dispell the energy by going STRAIGHT - the rein directs him to "go" on the curve. In other words, you "close the door" on the outside so he can't go straight, but you "open the door" to the inside curve and the horse goes in that direction.
This is a very pretty bend in a collected canter. You can see that the rider's outside leg is back, the left hand is set lower than the right hand, which is lifted to "close the door" on the outside. The horse is in the second beat of the canter (two diagonal legs on the ground). Note how the LH leg is placed well forward, showing that the hindquarters are collected (even though the single hind leg is trailing at the moment). The withers are higher than the quarters - the horse is nicely collected and lifted in front. Ideally the front of the horse's face should be exactly perpendicular to the ground - and this horse is pretty darned close. If the nose goes back too far, there's too much hand pressure and the horse is seeking to evade the bit by breaking at the poll. This horse is accepting the bit nicely, and he's happy (look at his ears!)
This pic is from the Dublin Horse Show - the cream of the crop.