I think it shows that Suyuan is apologizing to Jing-mei. The events in "Two Kinds" broke the relationship between mother and daughter. Suyuan pushed Jing-mei so far that Jing-mei wished that she was dead like the other daughters.
And I could sense her anger rising to its breaking point. I wanted see it spill over. And that's when I remembered the babies she had lost in China, the ones we never talked about. "Then I wish I'd never been born!" I shouted. “I wish I were dead! Like them."
Just a few lines before that, Jing-mei said that she wished that she wasn't her mother's daughter. It's a clear break in their relationship, and that break never quite healed. The sequence is a coming of age story, but it is also the story of a broken relationship.
I believe that Suyuan's gift of the piano is an olive branch of sorts. She is hoping for peace and forgiveness between the two of them again. She is forgiving Jing-mei for what was said.
I saw the offer as a sign of forgiveness, a tremendous burden removed.
The gift worked too. It seemed to melt away those years of bitterness and anger from Jing-mei. In the text, Jing-mei admits that seeing the piano now gives her sense of pride.