Scientists say, "magic." Almost. All right, so scientists actually say, "magic angle." To skip, the path of the stone must be at an angle of twenty degrees to the water. The question is, why is twenty degrees the best angle?
Sure, stones will skip if they come in at a shallower angle, but not as far. Chuck them in at an angle of greater than forty-five degrees and they'll just sink, sullenly into the water.
This has to do with the mechanics of the skip. Anyone who has practiced skipping stones across the water knows that the only stones that work are ones that are relatively light weight, and flat stones. The light weight part is obvious. A person would have to heave a pyramid block at a very precise twenty degrees to get it to skim across the ocean like a flying fish. (Which isn't to say it couldn't happen. Perhaps the mystery of the pyramids is that the Egyptians skimmed the stones into place by hopping them along the Nile. Probably not. But damn, what a mental image.)
(Pictured: A much less interesting way the pyramids might have been made.)
Stones also have to spinning like a Frisbee when they're thrown. The spin keeps the stone steady, like a gyroscope. The stone will keep flying in the same position, even when other forces push it around. The stone needs to hit the water with the front edge slightly higher than the back edge. Usually, this would cause the stone to flip over and sink into the water, but the spin keeps it facing up.
Because the back of the edge is in the water, it drags, raking up water in front of it. When the water builds up to a certain angle, the stone just slides up it like a ramp and keeps skipping. How long it skips depends on the velocity, spin, closeness to the ‘magic angle,' and whether or not "Follow the Yellow Brick Road," is playing.
Get it right and it might look like this: