Equilibration is a concept developed by Piaget that describes the cognitive balancing of new information with old knowledge. This is a major component of Piaget's theory of childhood cognitive development. Equilibration involves the assimilation of information to fit with an individual's own existing mental schemas and the accommodation of information by adapting it their way of thinking.
For example, a child loves the soups that their family eats on a regular basis. They have developed the schema that all soup is delicious. The child then has dinner at a friend's house and is served a bowl of soup- and hates it. Initially the child is in the assimilation area of Equilibration - they feel that since ALL soup is good then this soup must be good. They repeatedly keep trying it and disliking it. This leads to disEquilibration which is a state of cognitive conflict and stress. In order to alleviate the disEquilibration the child enters the accommodation phase of Equilibration - they adapt their thinking to stop the conflict and realize that not all soup is good and that some of it tastes bad.