Final answer:
The term describing adolescents' egocentrism with a sense of uniqueness and invincibility is 'personal fable.' It is a part of adolescents' psychosocial development involving identity formation and risk-taking behaviors.
Step-by-step explanation:
The term used to describe adolescents' egocentrism involving a sense of uniqueness and invincibility is "personal fable." During adolescence, individuals develop a sense of self through exploration and challenging existing roles. However, this process can sometimes lead to a belief in one's own uniqueness and invincibility, characteristics of what is termed the personal fable. This concept is a part of the psychosocial development in which adolescents continue refining their self-identity and developing a stronger sense of personal identity. The belief in their own uniqueness can lead teens to think that no one can understand them, while the sense of invincibility often results in risk-taking behaviors because they feel immune to the consequences that affect others.