The definition given in Webster’s Dictionary is “the art, science, or profession of teaching”.
Wikipedia provides the following definition for piano pedagogy.
Piano pedagogy is the study of the teaching of piano playing. Whereas the professional field of music education pertains to the teaching of music in school classrooms or group settings, piano pedagogy focuses on the teaching of musical skills to individual piano students. This is often done via private or semiprivate instructions, commonly referred to as piano lessons. The practitioners of piano pedagogy are called piano pedagogues, or simply, piano teachers.