The expanding animal-shaped toys are sold under a lot of different names, and don't seem to have a typical generic name, but a few science-experiment sites call them "grow creatures."
They are made of a hydrophilic ("water-loving") polymer called a hydrogel, similar to the absorbent chemical in modern disposable diapers. The hydrogel is combined with another polymer which is hydrophobic (not rabid, just "water-hating"), which causes the animal to hold its shape as it grows, and which helps it maintain its shape as it shrinks if removed from water.