What does Waverly's discussion with her mother about playing in a tournament suggest about Waverly's understanding of her mother's expections?

In "The Rules of the Game," a selection from Amy Tan's The Joy Luck Club, Waverly learns to play chess and also learns strategy from her mother just by observing the way her mother communicates and takes control of situations in her own life.
Waverly becomes quite skilled at chess and performs well in the exhibition tournaments, which her mother watches from the crowd. The pivotal moment in your question occurs about halfway through the story. Waverly explains,

A man who watched me play in the park suggested that my mother allow me to play in local chess tournaments. My mother smiled graciously, an answer that meant nothing. I desperately wanted to go, but I bit back my tongue. I knew she would not let me play among strangers. So as we walked home I said in a small voice that I didn't want to play in the local tournament. They would have American rules. If I lost, I would bring shame on my family.
"Is shame you fall down nobody push you," said my mother.

The man tells Waverly's mother that Waverly could do well in tournaments, which would have prizes and would be more formal competitions than the exhibition practice games. Waverly does not think her mother will approve, so she hedges and says she doesn't want to play, even though she "desperately wanted to go." To her surprise, Waverly's mother actually seems to support her participation in the tournaments. Her quote, "Is shame you fall down nobody push you," implies that Waverly will only bring shame to her family if she does not try. If she falls down without any push, she is lacking courage and that would be shameful. Waverly's conversation with her mother motivates her to sign up for the local tournaments, which her mother continues to attend and watch.