Piaget's theory of cognitive development describes a theory for how complex thought processes can be achieved by scaffolding up from more simpler ones, step by step, beginning with simple newborn reflexes which require no conscious effort, all the way up to complex abstract thought. If you want to nerd out on this, you can gain a better appreciation for this incremental process by reading into the substages (the Wikipedia article describes them). I qualify that with "if you want to nerd out", because detailed information about the substages is very likely unnecessary for nursing students and nurses.

It is, however, important to understand that this podcasts only cover the 4 main stages of Piaget's theory, but that is an incredibly low-resolution picture of cognitive development. Children do not hop from stage to stage in discrete steps, as if they were an evolving Pokemon or some kind of Dragonball Z villain. Even all the substages do an imperfect job of capturing how gradual a lot of these changes are. Transductive reasoning, for example, is not something that simply disappears after the 7th year of life - I'm sure many of the superstitions have come from adults following a very similar logical process. And yes, children in the concrete operational thinking stage need physical illustrations and struggle with abstract concepts, but so do I. If you benefit from a physical illustration rather than being thrown a bunch of abstract thoughts, that doesn't make you a grade schooler, it just makes you a normal person.

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I have seen many nursing students confuse Piaget's theory of cognitive development with Erikson's, and to a lesser extent Freud's, theories of development. It might be helpful to see Piaget's theory as directly concerned with the complexity of thought, with little concern as to its particular area of application. This actually has the side benefit in that Piaget's theory, when understood to the point that it can be applied, becomes a gift that keeps on giving.

For example, Piaget's theory serves as the foundation for Kohlberg's theory of moral development. Children who are egocentric only understand morality in terms of how it affects them, rather than an understanding of an abstract principles of morality like justice and equity. Those kinds of concepts will only be properly understood in the formal operational stage.

Or another example, if we wanted to gauge a child's understanding of the concept of death and mortality, we should expect egocentric thinkers to first be concerned with how the death of a person affects them. We should expect that preoperational thinkers may have inaccurate thoughts about death (e.g. thinking people can come back to life), because it's hard to achieve that kind of understanding through transductive reasoning.

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If you have no experience with children, then this theory will help you to gauge the cognitive ability of your child, especially when you are trying to decide how to explain what you are doing and why you are doing it.

If you do have experience with children, this theory will help you on tests, to calibrate your understanding to fit the child from NCLEX-land. You may have seen children move through these different stages at different speeds, and answer based on your personal experience, which may not match the theoretical numbers given by Piaget.