This study brings a hypothetical model of the structure, the formation and the training of activity as a personality’s quality. The authors regard activity as a complex quality, which is the result of a development of systems and fulfils the function of a regulator, decreases the variety of information from the vicinity to the system, increases and improves the self-regulation of the system. Activity, from the psychological point of view, includes, above all, the activity of character, of temperament, and the need for activity in their mutual interaction. The study summarizes briefly the knowledge about these components of activity, about their manifestations and their development in the ontogenesis. The formation of the activity of a personality is the result of an interaction of social influences, biological pre-requisites and the individual’s rising activity itself. The authors deal especially with the influences of the specific attitudes of the family, school and society to manifestations of the child’s activity, with the influences of social roles, with the example of using the time, with the tendency of young people to keep up with adults, with the solution of the contradiction between the child’s wishes and the actual performance of his or her favourite activities. The training of activity requires not only didactic measures (problem instruction and the like), but, above all, an opportunity for suitable activities and a motivation of children and young people (in personal contact of the educationalist with the pupil). The development of the activity of the personality is essential in the period of the scientific and technological revolution, especially in the developing socialist society.