The article shows the problems of improving the quality of Russian education related to the understanding of the essence of competencies. In spite of the constant «updates» of the Federal State Educational Standards for Higher Education (FES of HE), there is no obvious qualitative change in the solution of this problem. And first of all, it refers to what is not clear: what and how students should be taught, although the standards define that students should have the necessary competencies to perform a professional activity. However, despite numerous discussions, a clear understanding of the scientific essence of the concept of «competence», as a rule, is not given anywhere. And this today, in our opinion, is the main problem and obstacle in the qualitative improvement of the educational process in domestic universities.