"My potential is more than can be expressed within the bounds of my race or ethnic identity"

This quote by Arthur Ashe talks to the idea that a person's capacity is not limited by their race or ethnic identity. He is recommending that a person's capacity is much higher than what is normally anticipated of them based upon their race or ethnic background. He is motivating individuals to look beyond the boundaries of their race or ethnic background and to aim to reach their full potential. He is highlighting that a person's capacity is not identified by their race or ethnicity, but rather by their own private abilities and talents. He is suggesting that everyone has the potential to achieve achievement, no matter their race or ethnicity. He is motivating people to break down the barriers of race and ethnicity and to aim to reach their full capacity. He is advising us that we all have the potential to attain achievement, despite our race or ethnic culture.