She wants to share in her daughter’s accomplishments.
Explanation:
By reading only this passage we can infer that the reason the mother's narrator introduces her to everyone is because she is very proud of her daughter. Therefore she wants everyone to know her and her accomplishments. The narrator states that her parents made concessions so she can practice, she also had to "accompany" her mother when she had no tournament to play; we can infer that she is a very talented athlete and her parents expect a lot from her. It is very probable that they visit a local market where everyone knows everyone so it's reasonable that the mother introduces her daughter.
