In a lot of Clinton's exercises it all starts from the ground. Whenever I can teach a horse something from the ground first, it will make my job a lot easier in the saddle as well as safer.
Flexing is where I can pick up on the reins lightly and flex the horse's head to where his nose towards the girth where he is either touching his belly or my leg/foot if I'm in the saddle. It should be light enough to where I can use two fingers on reins with no stiffness.
I teach this from the ground first before I do it in the saddle. This helps the horse get softer laterally as well as respect. Horses don't have hard mouths, they have hard stiff bodies. I'm working on getting my horse soft throughout his whole body (not just his head). There's five body parts of the horse that the method goes through to soften: Head and neck, poll shoulders, ribcage and hindquarters. Here's a picture of Sugar and parts of her body:
By teaching flexing it softens the horse's head and neck. A lot of the time a horse's first reaction will be to push against any pressure in the bit. Teaching the flexing teaches him to respect you more when controlling his head and softens his neck. And it's also very useful in spooking situations.. XD