There are 3 important issues which I feel are important to the individual or parents

1. The ability to play a piece or pieces effectively and technically sound.
2. To be able to play and learn songs that the student likes or enjoy playing. After all it is for relaxing and recreation that is what the student wants.
3. To learn styling techniques, accompaniment styles, improvisational skills so that the student can showcase his or her skills on the piano. To be able to perform and play to entertain family members or friends.

Throughout 40 yrs of teaching and performing myself as a pianist, I see what students are looking for and what they want. Today students and parents want Popular music that they like and can understand, which I teach. Some are even curious about Jazz music which I teach too. Finally, many students question about Harmony, Chords and Accompaniment or voicing of parts which I explain fully too, since this  is a common subject of many questions.