We find the answer to your question at the beginning of this short story that comments so much on the experience of migration coming from the point of view of Chinese immigrants to America and the conflict that occurs between these immigrants and their children, who are born in America and thus grow up learning very different values from their Chinese parents. Thus it is that Waverly, the protagonist and narrator of this short story, possesses a strange hybrid mix of values and lessons she has learned, some from her Chinese heritage taught to her by her mother, and some from her American heritage: her birth country.
The art of invisible strength, then, is part of Waverly's Chinese heritage:
I was six when my mother taught me the art of invisible strength. It was a strategy for winning arguments, respect from others, and eventually, though neither of us knew it at the time, chess games.
This "art of invisible strength" is described by her mother as not confronting others openly. Instead, you must seem to go along with them whilst subtly leading them in the direction that you prefer.
This is a good question. The above answer does a good job, but there is more. When Waverly was six years old, her mother began to teach her the art of invisible strength. According to Waverly, the art of invisible strength was a strategy that allowed her to win arguments and respect from others. Waverly's mother put it in these words:
"Wise guy, he not go against wind. In Chinese we say, Come from South, blow with wind-poom!-North will follow. Strongest wind cannot be seen."
Waverly's mother probably came to these conclusions as a Chinese woman who had to survive in a new world and land. She needed to be shrewd, wise, and even manipulative at times. She needed more than brute force; she needed invisible strength, an element of surprise.
As the story progresses, Waverly also commented that the art of invisible strength was very helpful to her in her passion for chess. Finally, Waverly used this art to counter her mother.