The movie is based on a novel by Nobel prize winner Elfriede Jelinek. Haneke adapted the screenplay and, based on his interviews, has changed the behavior of some characters.
There is some judgment of value in this movie's title. By calling the pianist a piano player, the author seems to be referring to the frustrated career of the teacher as a piano soloist.
A Piano teacher gets involved in destructive sexual games with one of her students. She takes special pleasure in torturing him and on trying to force him into a masochistic relationship. The origins of the teacher's behavior relate to her very destructive relationship with her mother. And the story can, in some sense, be considered a love triangle. The interaction with the teacher makes the student more and more frustrated, and at some point, he beats and sexually violates her.
As she has already been shown mutilating herself, it might be that the relation with the student has just precipitated in her something that was innevitable. The final scene, where she quietly stabs her heart, and is shown leaving the building where she would play the piano and out of the picture is of extreme beauty. The story can't be resolved, the viewer is left with questions hanging. Some of my questions are:
"Could anything have saved this woman?"
"Given our life histories and different expectations on relationships, can love be possible?"