I love this question! It is so wide open, yet every day, piano teachers grapple with the enormity of what they want to offer their students. There are so many ways to go with this, but I want to share my philosophy.
I have always said that if I have three to five years with a student (any additional years is like gravy), it is my job to teach them how to read music, how to count and express emotions, understand terminology, and hopefully impart the love of not only the piano, but music. Now, you may think that is quite a long time to spend on these basic concepts, but in reality, it is not. Oh sure, an average aged beginning student (6-7 years old) can grasp reading on the staff and counting simple rhythms, but that is not enough. I generally takes about three years, before a student is confident and able to internalize reading and counting skills. Regardless of what the end result is, as a teacher, I want my students to leave my studio and be able to pick up a piece of sheet music, hymnal, lead line and be able to play until their heart is content. So, what do YOU want your students to know?