An important aspect of child psychology is how children’s understanding of the world develops. For example, children develop a conception of themselves as individuals, of other people as members of their family or people outside their family, of physical laws (if you drop a glass, it breaks), and so on.
One of the key stages of conceptual development is developing the idea of object permanence. Very young babies do not attempt to look for an attractive object which is hidden. As they grow older, they understand that the object still exists and they look for it.
Other key ideas in conceptual development are pattern recognition (learning to recognize and eventually to predict patterns) and abstract operations (learning to think in abstract terms, using abstract language).