When Vince Offer was trying to sell you a Shamwow and said Olympic divers use them, he wasn't just being a blowhard. He was being a blowhard who had his facts straight, more or less. You might have noticed that Olympic divers in Rio aren't using a nice soft towel, but a tiny towel they are fine leaving over their shoulder while they shower.
They're actually using shammys, like a dad who is a little too concerned about water spots on his new car. Those rayon or poly-vinyl towels are capable of holding 10 times their weight in water and dry out almost instantly after they're rung out.
And that's what it's all about for divers: Finding a way to get completely dry between dives.
In a dive, the athlete is often gripping their legs or other body parts. If their legs are wet it can be difficult to get a good grip, raising the possibility that their hands will slip. Slipping can mean losing control mid-dive and it can mean lost points.
Using a shammy helps the diver to get their hands and legs almost completely dry, leaving them just moist enough to get a good grip. It's a routine done by all divers. It became standard practice in the '60s and '70s when some Norwegian and European divers began to use them.