Yeah, reminding me this has to do with conservation of momentum across vectors or something like that to redirect the energy of your fall in another direction. And right, you need more dimensions so all of the falling body isn’t hitting the ground at the same time.
I did this myself in desperation a few years ago. I Have a bad knee and stepped off a low platform while painting. Only about 15 inches high but in the short time it took to drop I knew it was going to be bad. As soon as I touched down I pitched sideways onto my shoulder (I still had things in my hand). I still limped for a few days but it wasn’t catastrophic. At the time I couldn’t step off a curb without holding on to something.
So the top of my body which would have just stopped and the weight crushed my knee went sideways in an arc and my shoulder took a lot of the force.
And every day from then on in 
Judo of course assumes than the fall is largely initiated by your opponent, and can occur in any direction. Most forward techniques involve uke doing a 270 from standing to lying on the floor. So a break-fall involves a roll and a lot of energy and to dissipate, and momentum to manage, as one hits. Slapping the mat is a curious but effective part of the technique, and seems to be a pro-active transfer of momentum back into the Earth before the main body hits. Done right in a rolling breakfall and it helps greatly in continuing the roll to stand stright up again.
Many years ago one of our club members came of her motorbike at speed. She just rolling down the road as a continuing breakfall. Then got up, shaken, a bit bruised, but otherwise fine.
The forward breakfall emphasises a position that protects the spine and avoids the head contacting the ground, and positions the arms and legs to adsorb energy with minimal damage. Avoiding bony bits contacting the ground and adsorbing energy with flat areas of flesh.
Eventually one is expected to do this instinctively, as in competition your opponent is not going to give you the slightest warning of executing the throw. Sometimes one finds oneself on the mat with no idea what just happened. Thinking is bad. People do silly things like putting their hand down. Then it is a trip to ER to have bits of ligament put back together.
Kinda related, but several years back I happened to have 2 cases pretty close to each other in which people injured themselves falling from a modest height. One tried to kill himself jumping off an overpass into traffic, and the other was fucked up and either fell/jumped off a roof.
They both landed on their feet and incurred IDENTICAL injuries. Multiple fractures to both legs, and a vertebral fracture where a couple of their vertebrae (I forget which) essentially exploded.
I figured the area ought to either construct taller structures or teach diving lessons… 