When Fathers and Sons was first released in 1862, members of the younger generation were outraged because they thought that Turgenev was parodying them through the character of Bazarov. From time to time, we hit upon a line where we understand what they were worried about. For example, when Bazarov dismisses love between a man and a woman, he says, "That's all romantic rot, mouldy aesthetics. We had much better go and inspect that beetle" (7.19). Reading that line, it's hard to imagine an intelligent young man who wouldn't be self-aware enough to realize how ridiculous he sounds. One imagines that the narrator (or the author himself) is having fun with Bazarov.
Yet, as the novel goes on, it becomes clear that the narrator writes about each of his characters with supreme sympathy. His main goal is to depict the situation carefully and truthfully, not to pass judgment on his characters or to mock them. As for the notion that Bazarov is nothing but a parody, Turgenev claimed that he wept as he wrote Bazarov's final death scene – that is how attached he had become to his character (Isaiah Berlin, "1970 Romanes Lecture"). When we read Bazarov's last words, it's hard to imagine a parodic figure that could give voice to such a beautiful line, "Breathe on the dying flame and let it go out..." (27.151). It's almost as if Bazarov has taken on his own vitality and he is speaking not only to Anna Sergeyevna, but also to the narrator, telling him that it is OK to let him die (note that this is just a metaphor, so don't take the idea too literally).
Now, since Turgenev's watchword was realism, the narrator often seems to keep the story at arm's length from himself. It's as if he doesn't want it to become too imbued with his own personality. Yet, at times he cannot help himself. It is clear that even if the narrator is trying to render his story truthfully, he cannot maintain a scientific detachment from his material (not so different from how Bazarov cannot remain detached from his own life). At one point the narrator erupts, "Is there anything in the world more captivating than a beautiful young mother with a healthy child in her arms?" (8.24). Such lines make it clear that the narrator is invested in the story that he tells. Perhaps he does his best to keep himself out of it, but at times his enthusiasm breaks the narrative bounds and he inserts himself into the story (see "What's Up with the Ending?" for the most obvious example of this self-insertion).