Universality as a broad concept means that something is universal- it exists in all conditions all over. For example, something that has universal appeal is liked by everyone. Universal implies that it is true throughout the entire universe. In psychology the term universality was used by Gordon Allport) in regards to his trait theory of personality.
Allport attempted to explain personality as answering the question of uniqueness versus universality. He believed that the study of personality could be characterized in 2 ways: nomothetic (universal traits of personality that can be generalized to large amounts and types of people) and idiographic (characteristics that are unique to the individual).