Waverly's mother wants desperately for her daughter to be not only successful but to excel above all others.  Waverly chooses to play chess to "excel," and her mother's comment is in response to Waverly's question about an instruction book she is reading on the game.  Her mothers explains,

"This American rules . . . Every time people come from foreign country, must know rules. You not know, judge say, 'Too bad, go back.' They not telling you why so you can use their way go forward. They say, 'Don't know why, you find out yourself.' But they knowing all the time. Better you take it, find out why yourself."

While Waverly's mom is answering Waverly's specific question, she is also speaking about life, especially the life of an immigrant in America.  Chess, in a sense here, is a metaphor for life.  Waverly's mom feels that no one told her the "strategy" for surviving in America.  She alone had to figure out what her next move would be.  This is why she is not very helpful or encouraging to her daughter.  She had to learn the hard way, and she wants her daughter to learn on her own, not by depending on others.