Any time you give an aid, there is an end to that aid in order to give the horse a chance to respond. The clinician is likely emphasizing that "end", when you should relax whatever aid you just used. For example, a half-halt, you hold in your abs and seat for half a second or however long is needed, and then relax. You don't have to make it more complicated. The clinician is probably stressing it because some folks, myself included, sometimes forget to relax after asking for something, but if you keep asking, the horse never has a chance to respond.
If you put your hand/arm forward to finish an aid, you are throwing away whatever you just asked for.
OP - that clinician called it softening; my trainer calls it breathing. I think of it as a relaxing of the fingers on the reins, resulting in just the slightest easing of tension w/ out losing the contact.
We don't get less brave; we get a bigger sense of self-preservation........
Think of it as going from a neutral position, asking "half halt" please, then back to the neutral position when the horse answers. As Nestor said, if you give the contact away you lose "revving" of the half halt. The horse is asking "What now, I guess I should maybe stop, transition up, stretch down or lengthen my neck, please tell me what you want".
"I've spent most of my life riding horses. The rest I've just wasted". - Anonymous
Sometimes when you halfhalt you close your fingers for a fraction of a second, as you hold in your core for a heart beat. You must relax those fingers, and go back to quiet conversation. Sometimes just stopping your body for the instant is sufficient and you needn't even use your fingers. That depends on you and how attentive your horse is.
Some riders change their horse, they change their saddle, they change their teacher; they never change themselves.
Remember the horse does all the work, we just sit there and look pretty.