Th narrator's reaction to pain and human loss is to shut down emotionally. For example, he cuts Sonny off until the polio death of his own young daughter brings a pain he can't deny. This causes him to reach out again to his brother. As the narrator says:
My trouble made his real.
The narrator has also reacted to his pain by rigidly fashioning a new, middle class life for himself as a school teacher, husband, and father. He escapes the Harlem ghetto and tries to shut out the haunting reminders of the past by behaving responsibly.
Sonny, in contrast, uses drugs to ease his sense of pain and loss, which is how he lands in prison. However, he says that drugs have never really worked against his pain. More constructively, music is his true and best antidote to suffering. Musically talented, he can express his pain, process it, and lose it in the momentary joy of creation when he performs jazz. Jazz is what gives Sonny's life meaning.
As the narrator comes to understand how music functions in his brother's life, he begins to grow less judgmental of him. He comes to hear him at a jazz club and realizes that Sonny is expressing all of humanity's pain and triumph through his music. The relief may be only momentary, but the narrator understands why music matters so much to his brother.