You have asked rather a broad question, so I have included links below to the relevant study section of enotes on this short story to help you gain further information about it.
"Two Kinds" is actually taken from a novel by Amy Tan called The Joy Luck Club, which follows the fortunes of four Chinese immigrants to the United States and their relations with their daughters. Of course, the fact that their daughters are born in the United States creates a conflict, as their mothers maintain traditional Chinese values and expectations of their children and their daughters grow up learning the American way of life.
This conflict is at the centre of "Two Kinds," as Jing-Mei faces the overwhelming pressure of her mother for her to become a "prodigy" and to gain fame and status through her talents. Thus it is that Jing-Mei is forced into having piano lessons with a deaf piano teacher, with disastrous results. At its heart, this excellent short story is about Jing-Mei's struggle to be accepted by her mother for who she is, rather than who her mother would like her to be. Her success in this is indicated by the way in which her mother gives her the piano that had been the sight of their bitterest conflict, which Jing-Mei calls her own "shiny trophy," indicating the way that she believes she has won it on her own terms.
"Two Kinds" is a short story by 20th Century Chinese-American author Amy Tan. It tells the story of a young girl named Ni-Kan. Ni-Kan is the child of a woman to emigrated to the United States after losing everything (including two daughters) in her home country of China. Ni Kan's mother is intensely proud of her only surviving child, and she wants her to become a child prodigy. The story then details all of the many types of prodigy that Ni Kan's mother had hoped her child might become, and it reaches its climax when Ni Kan's own wishes and behavior find themselves in direct conflict with the wishes and aspirations of her mother.
This is a quick, easy story to read, and it explores issues of family and self in conflict.