Think it is the same as the "planing" effect in a small speedboat. When
you drive a reasonably light boat at a good speed, it rises up out of
the water and seems to skim the surface (on a "plane"). It only works if
the prow is up and I'm pretty sure is because of the water hitting the
tilted bottom of the boat and rebounding downward, thus, from third law,
a force on the boat upward. Same true for skis. Nose of skis are bent
upwards to facilitate this. Water hits skis and rebounds down, pushing
skis (and skier) up.