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Music theory a vital aspect of the art of piano, which is often misunderstood and overlooked by pianists and teachers. The term "music theory" has different meaning depending on who is talking about it. (For example, "music theory" for an 8-year-old student is entirely different than "music theory" for a Ph.D. student.) When we talk about "music theory," at least for our purposes, we are usually referring to the harmonies or chords produced at the piano, which is often referred to as simply "harmony." Sometimes "music theory" can also refer to the rhythmic aspects of music.
Regardless of what term one uses, a "well-rounded pianist" should know the names and relationships (i.e., functions) of all the chords one plays. "Well-rounded" pianists who are adept at musical harmony are almost always better interpreters and sight-readers than "non-well-rounded" pianists, thus it makes sense to equip oneself with as much theoretical knowledge as possible. Moreover, a good working knowledge of music theory is mandatory for pianists who desire to write popular songs or compose in a serious classical style. Dr. Cory Hall (aka, "Cory") has a very strong background in music theory and composition in addition to performance, and has a special gift in explaining theoretical concepts to all levels of students, from children to adults.
Please enjoy two of Cory's music theory videos on YouTube -- 1) Authentic Cadences for Beginners; 2) Playing 3:4 Polyrhythms for Advanced Students