The most obvious symbol in the story is the game of chess.  At first chess is merely a game. One of Waverly's brothers received a chess set from the local baptist church for a Christmas gift. They play half-heartedly; however, Waverly takes great interest and she excels. In fact, Waverly gains national recognition. 

The underlying and more important story is really about the relationship between Waverly and her mother, Mrs. Jong. Waverly wants more independence, but. Mrs. Jong is not willing to let her go. When they have a conflict, Waverly sees her relationship with her mother as a game of chess.  Her mother's men advance and knock down her men.  

Her black men advanced across the plane, slowly marching to each successive level as a single unit. My white pieces screamed as they scurried and fell off the board one by one. As her men drew closer to my edge, I felt myself growing light...I closed my eyes and pondered my next move.

Another symbol is the fish and turtle at the fish market.  As Waverly looks at them, she sees that they are trapped in glass. They have little freedom.  This might symbolically refer to Waverly's life.