With the italicized sections of "Barn Burning," Faulkner is using a Modernist style of narration called perspectivism. In this style, the narrator is omniscient only in regard to one character, at least for a given part of the story where the technique is used. Thus the action of "Barn Burning" is experienced through the boy Sarty's perspective, and events are interpreted through the way he perceives them. The italicized portions of the story take us deep into Sarty's psyche and usually give words to either the conflicts he is experiencing or the hopes he has for resolving those conflicts.
As the story opens and Abner Snopes appears before a Justice for burning a barn, Sarty's thoughts voice his loyalty to his father, but the intensity of their expression indicate that the loyalty requires effort on Sarty's part. As they ride away in their wagon, Sarty begins to hope: "Maybe he's done satisfied now, now that he has..." As yet he cannot admit what his father did, but he hopes his father will change.
The next section of italicized thoughts occurs when Sarty sees the de Spain mansion. Interestingly, although Faulkner begins the section in Sarty's dialect with "hit's big as a courthouse," he goes on to convey Sarty's thoughts in expressions that "he could not have thought into words." This has the effect of giving Sarty a depth of understanding that his rustic speech would not have been able to portray while causing readers to feel the respect and empathy for Sarty that they would have for a more eloquent speaker: "the spell of this peace and dignity rendering even the barns and stable and cribs which belong to it impervious to the puny flames he might contrive." Although one could say Faulkner "cheats" here by giving Sarty an unrealistic inner monologue, it serves to separate him from the crassness of Abner and breaks the bond of loyalty that Sarty had previously fought to retain.
The next passages again reflect Sarty's hopes that Abner will change, but readers now understand his hopes are vain. Finally, Sarty thinks, as he runs to get the oil for his father to burn the de Spain barn, that he could run, but he concludes, "Only I can't. I can't." Just as Sarty's protestations of loyalty turned to disloyalty and his hopes for his father's reformation have turned to despair, so this claim that he can't run away foreshadows the very act he says he can't do.
Sarty's internal monologues allow readers to enter into the conflict of the story and to experience the growth of Sarty from unwilling loyalty to hope to rejection of his father's despicable behavior.