I believe elastic contact is what we might be trying to get at here.
The horse should not meet resistanceor a wall when asked to stretch forward into the bit, he should meet an elastic contact which allows him to move freely forward, but also helps maintain the connection and roundness. Contact is taking a feel of the bit with our hands (this does not mean see-sawing, pulling, or even sponging; it means making the hand an extention of the rein, as if we were directly holding on to the bit rings, and knowing when to give or take and when to be passive, or still). The elasticity is the looseness of our elbows and biceps that follow the natural movement of the horse's head as he moves and stretches (keyword is natural; not bobbing or other movements caused by rider issues, training faults, etcetera. These issues must be resolved).
We are not holding our hands in place, which creates inconsistant contact (the horse meets a wall), but not moving our hands manually with each stride either, which also creates inconsistant contact (makes it busy and destroys the meaning of a rewarding give). We allow the horse's head to "carry" our hands and arms, which are flexible, supple, soft, and light (like a bouncy elastic, hence the name), just like how we wish the horse's head to be. We give purposely when nessecary (a reward) and take if needed (to correct or shift position). Elastic contact can't be achieved without the rider first developing independent hands, and the horse must be willing to seek and stretch (not lean!) into the bit when we ask. It is probably one of the most difficult and elusive elements of riding to learn and make natural, for both rider and horse.
But none of this can ever happen if not accompanied by our other aids, working in balance and harmony. The horse must be appropriately working through, from back to front, before the headset is developed into the appropriate degree.
I hope that made sense. It's not easy to explain! Maybe this video can do better?