The "point" or main theme of "Sonny's Blues" has to do with the nature of human connection, how people grow over time, and how art, or more specifically music, can express these meanings. Sonny is a a drug addict and ex-con; his brother, the narrator of the story, has gone to college and attained a middle-class lifestyle and is a teacher. The story is mostly a series of episodes the narrator remembers about Sonny, in which we learn more and more about Sonny and what drives him. The reader shares this point of view: like the narrator, Sonny is a kind of tragic mystery that we learn more about as the story progresses.
Also like the narrator, the reader is put in a position of judging Sonny. The degree to which Sonny's addiction and incarceration are his fault or the result of a fundamentally racist society is a kind of open question. As we learn more about Sonny, however, we begin to see him less as a stereotype and more as a fully formed human. Characteristically, when Sonny tells his brother about his plan to become a musician, the narrator thinks he is not serious. But when he finally goes to see his brother play at a club, it is a revelation for the narrator.
Sonny's music shows that his life experiences have made it possible for him to create great art. With this realization comes the notion that Sonny's life, however troubled it may have been, has been worth living.