Egocentricity refers to 'self-centered', an interest in oneself to the point of excluding any interest in other people.
In Piaget's theory of development the term does not have any pejorative connotation of selfishness but refers to a stage that lasts until the age of 7 or 8, where a child is unable to adopt someone else's perceptual frame of reference and see a situation through his eyes. Thus a child at this stage is unable to describe what an object looks like to someone sitting across the table from him-he describes it the way it appears to him.
The child's conceptual, cognitive world is similarly egocentric. A ‘foreigner’, for instance, is always a foreigner, even in his own country, but the child himself is never a foreigner even in someone else's country. This stage ends when the child achieves reciprocity, though egocentric behaviour can often be observed in adults.