The Fosbury Flop came into the High Jumping scene in the 1968 Olympics, where Dick Fosbury used the technique to win the gold medal. The biggest difference between the Flop and previous methods is that the jumper goes over the bar upside down (facing the sky). This allows the jumper to bend their back so that their arms and legs drape below the bar
It is significant that Fosbury is not modeled as a sphere.
I guess the best explanation for how it works is that it is like a giant see-saw. When people jump down on one side of the huge airbag, the other side goes up. If you consider small energy losses, then the work done by the bag in slowing the falling people down is the same work done on the launched person.