The importance of the topic of the article is that nowadays there is a need to update methods and techniques of teaching in the educational process, the use of innovations in student teaching, because it is not important how much knowledge a student receives, but how one can use them in practice. The purpose of the article is the need to study and justify the importance of studying the essence of the concepts of “the competence” and “the competency” in the system of psychological and pedagogical categories. The article gives a theoretical justification for the concepts of “competence” and “competency” of the teacher in the pedagogical context; the similarity and difference of the concepts “the competence” and “the competency” in the system of psychological and pedagogical categories are investigated; the concept of professional competency and its categorical essence as a set of professional knowledge, skills, abilities necessary for both teachers and students in the XXI century is given. Nowadays, the purpose of school education is determined by the entirety of knowledge, skills and abilities that a student shouldacquire. In the XXI century, such a perspective is insufficient for society, because professional educational institutions, industry, families do not need weisenheimers, but graduates who are ready tointegrate in the real life, who have the ability to quickly and easily approach life and professional problems, which appear before them, so that getting into a problem situation, they could find several ways to solve it, to choose a practical way, justifying one’s decision.