The unnamed narrator is important to the story not just because it's through his perspective that we get the narrative, but also because he provides us with an alternative view of Sonny's life. Through the narrator we get to see how Sonny's drug addiction affects those around him and how difficult it is for someone who isn't a musician (which is probably most readers) to understand what motivates someone who is. It's almost necessary that we hear the story from the narrator, since Sonny would have been an unreliable narrator himself. That said, the narrator certainly has his own biases and opinions; he's not an entirely neutral voice.
In many ways the narrator is the voice of reason throughout the story. He tries to get Sonny to think about his future and he basically becomes Sonny's father figure once their parents have passed away. Although he doesn't really understand Sonny or his passion for music, he does have Sonny's best interests at heart. Deep down, we think he's a pretty good guy.
But the narrator is not without his faults. We could argue that he abandons Sonny when Sonny needs him the most. And perhaps, as Sonny suspects, the narrator is really just upset that Sonny has chosen a life that's different from his own. Maybe the narrator is too guided by rules and by doing what he thinks he's supposed to do. (What do you think it means that he's a math teacher? Hmm.)
So there are things we really like about the narrator and things that bug us, too. We think that's what makes him relatable. He's not perfect – he's human. He doesn't know how to deal with Sonny's problems (who would?) but he tries his best. He does what he can and what he thinks is right. And in the end, he tries to meet Sonny half way. Literary folks would say that he's a dynamic character because he undergoes a noticeable change from the beginning of the story to the end. This change happens because he at least tries to gain some understanding of his brother.Timeline