Let us remember that a symbol is an object that stands both for itself and some kind of larger idea or concept. When we look at the piano in this story therefore it is important that we think of what larger ideas it represents above and beyond itself.
It becomes clear that the piano is very symbolically important in the relationship between Pol and Bayard. Although Pol finds her husband's silence and non-communicativeness greatly challenging, the piano seems to represent their one emotional and loving connection. We are told in the novel that Pol is a very skillful musician, and that when they were younger Bayard greatly loved to place himself behind her whilst she played and listen to her music. To celebrate their wedding, Bayard bought her a piano and Billie Jo reports to us that when he stood behind her his eyes "grew soft."
The piano therefore symbolically represents the love that Pol and Bayard have for each other, in spite of their many problems. In addition, we can see that the piano is a symbol that changes in terms of its significance, as Billie Jo takes on her mother's talent and becomes a skilled performer in her own right.