The symbolism of "the piano lesson" in the story is the lesson of history itself.  Wilson explores the themes of African-American identity and the struggle for civil rights.  In this story, he incorporates specific reference to the legacy of slavery.  While for most modern Americans, slavery is a distant event, for many African-Americans the legacy is a living part of their lives and their relationship to others.  History varies based on who is telling it or who is living it - perspective influences an individual's understanding of an event.  In this story, each family member wants the piano for a different reason, symbolizing this idea of perspective.