Cat urine is not much different from any other urine, be it human or other animals. It is made up urea, creatinine, uric acid, sodium and other electrolytes. The uric acid is what makes it smell so bad and cats not being big water drinkers have concentrated urine and so the uric acid also is more concentrated.

When cat urine dries the urea gets broken down by bacteria which gives it that distinctive ammonia smell. As it decomposes further it releases thiols which make the cat urine odor worse yet.

The recipe works because the reaction of hydrogen peroxide and baking soda produces large amount of oxygen. The oxygen molecules bond to the thiols, breaking them up into carbon dioxide and ammonia, that evaporates quickly thereby effectively neutralizing the thoils and their foul-smelling odor.