This article stresses the social importance of the problem of giftedness and in this connection the necessity to clarify this concept scientifically. The history of this problem reveals the origins of reduction of the concept and the wide-spread notion of giftedness as "intelligence level above average. "There are two reasons of it: 1) Galton's components of giftedness were put into a complex; 2) there were no measuring techniques of this complex. The unit of the analysis of giftedness was formed after Galton's notion of giftedness as comprised of components was supplemented with the method of measurement -"systematic observation"- and understood as an ability to generate activity at one's own initiative. Then it became possible to realize Galton's concept of giftedness as a manifestation of mind and character.