The concept “quality of education” is widely used in modern educational practice; however, in teaching, there is no common understanding of the pedagogical phenomenon that underlies this concept. In this regard, it is necessary to present reflections on the content of such terms as “education” and “quality” in relation to the cultural and historical prerequisites for the formation of the category “quality of education” and various approaches to its content. Besides, the article touches upon different approaches to the procedures for measuring the quality of education and distinguishes their strengths and weaknesses. The authors encourage the reader to think about the problems of defining the quality of education as a pedagogical phenomenon in modern conditions through cultural and historical traditions. The study results in the consideration of various aspects of the evolution of such terms as “quality” and “education” in Russian pedagogy, which have influenced the modern interpretations of the concept “quality of education” and the approaches to its measurements. The article reveals the advantages of a practical understanding of the quality of education, as well as the risks associated with the transformation of education into a service and the absolutization of its quantitative parameters in measuring the quality of education. The authors raise the questions that remain open and require their solution despite the continued interest in the problems of education quality in pedagogical theory and practice. The novelty of the research is provided by taking into consideration Russian cultural and historical traditions of the formation of such terms as “education” and “quality” and the justification of the possible ways of their use in modern approaches to the measurements of quality of education, as well as the justification of the importance of using the applied aspect of the quality of education in Russian educational practice.