Since I've been a "waist bender" all my life, even with picking things off the floor I'll try to explain what happens. When I bend from the waist my hips push back and my shoulders align around the middle of my thighs. The only way I can get my shoulders over my toes, no matter how much I bend my ankles, is to move my upper body forward and down. But then I'm in an extreme, crunched position with the upper body. My legs can't move freely. If I hinge from the hips I'm free to move my upper and lower body independently. This is what my trainer meant when he said I have to learn to disassociate my legs from my torso.
However, this did not come easily to me. My first attempts at toe touching were very strange. It felt like my head was "very far away from my legs". I had to practice the movement every time I bent over. For awhile I was in a state of confusion with my body. Every movement was confusing. Then I saw the cue, " hips move 1st, then upper body". I use that cue when I ski.
Like Bounceswoosh and Abbi are saying hip hinging is a more stable position, takes the stress off the lower back and allows the legs to move freely. However, it's easy to revert back to bending at the waist while skiing in more difficult conditions.
The hip hinge is a basic human movement. How many kids do you know that don't hip hinge? Watch them on skis. I haven't seen one that doesn't hinge at the hips. That"s why it was the 1st thing my trainer taught me. It's an important move for deadlifting, kettle bell swings, everything he has me do. It's also an import movement for life. Unfortunately, this is often over looked by health professionals. I can't tell you how many times I've asked my PT's why my low back hurts and have been told "I don't know" and yet they didn't check my toe touch.
Now when someone mentions "stack your joints, or athletic stance", I just smile and think to myself, I know what they're talking about.