Imagine you have two boxes of lego blocks, one box is purple (cerium(iii) oxide) and the other box is green (cerium(iv) oxide). If you take apart the lego creations in the purple box, you'll end up with a bunch of individual blocks. But when you put those blocks back together in a certain way, you'll end up with the green lego creations in the other box.
Similarly, cerium(iii) oxide and cerium(iv) oxide are two kinds of materials that are made up of slightly different building blocks (atoms). When cerium(iii) oxide is exposed to high temperatures, it breaks apart into smaller pieces (atoms) and rearranges itself to form cerium(iv) oxide. This is like taking apart the purple lego creations and putting it together to form the green lego creations.
But when the cerium(iv) oxide is then exposed to water, it breaks apart again and rearranges itself to form cerium(iii) oxide once more. This is similar to taking apart the green lego creations and putting it back together to form the purple lego creations.
This back-and-forth process of converting cerium(iii) oxide to cerium(iv) oxide and back again is called the cerium(iv) oxide-cerium(iii) oxide cycle. Scientists use this cycle for various applications, such as in the production of fuel, as a catalyst in chemical reactions, and even in self-cleaning ovens!