Actually, cats really are alive and dead at the same time according to the many worlds interpretation. Under classical quantum mechanics, we say that superpositions collapse when observed, and since the cat is an observer of the quantum event (since the cat would die if the atom decayed), then the cat's presence resolves the superposition. Thus, the cat is never in superposition.

However, according to the many worlds interpretation, observation does not collapse superposition. Rather, it simply expands the superposition to include the observer. So the cat, as an observer of the quantum event, really is both alive and dead. And at the moment that you open the box to see whether the cat died, you will also observe the quantum event and become part of the superposition as well. You will both see a dead cat, and see a living cat. But your consciousness only experiences one of these possibilities. Presumably, you have another consciousness in the other possibility observing the cat in the other state. Two separate timelines have been created, which will each progress on their own according to causality. We may also call these timelines worlds or universes, seeing as they're mostly self contained.