You know those little plastic fish that appear to magically writhe and flop when you put them in the palm of your hand? Supposedly the way they move will predict your future. But in reality, you'll have literally as much luck prognosticating with these fish as you would with a diaper. In fact, the same chemical that makes these fish hop around is what makes diapers so absorbant. It's called sodium polyacrylate, aka waterlock.
Something called "waterlock" is exactly the kind of thing that you'd want in diapers, but it wouldn't do any good to most fish. Waterlock has long strings of acrylate compounds that have a positive charge. This charge tempts water molecules over to them. The water molecules lock on to each compound, allowing the overall chain to take hold of many times its own mass of water. Obviously, this is the kind of thing that would go well in a diaper.
One of the reasons it's so perfect as diaper material is a diaper isn't supposed to lie flat. It's not a fashion accessory. It can deform whenever it needs to. As the sodium polyacrylate absorbs water it deforms, especially if the water is unevenly applied. The same thing happens with the fish. The different amounts of moisture on the different sections of your hand will be absorbed by the material in the flat fish, warping it. The warp presses the remaining sections of the fish more firmly against your hand and causes it to warp and twitch even more.
Dry a fish out completely, and it'll go right back to flat, which means the fish are reusable. That's one thing they've got over diapers.