The three forms of point of view are first person, second person, and third person (of which first and third person are by far the most common). In first person the story is told from the perspective of a character within the story while in third person, the narrator exists outside of the events of the story. "Soldier's Home" was written in third person point of view.
Had this story been written in first person point of view, you would have expected this story to have been told by one of the characters within it: perhaps Krebs (returning from war), his mother, or his sister, and this person's perspectives, agendas, and personality would have shaped the story as it is told. Therein lies the great strength of first person voice: by transporting the reader into the mind of a character, it becomes the most subjective and personal of the narrative voices.
As for "Soldier's Home," this is a story written in a particularly unique form of third person perspective. Usually, third person is sub-divided into two kinds of narrative voices: third person limited and third person omniscient. In third person limited, the narrator is tied directly to the perspective of one character within the story (the Harry Potter books is an example of this form of narration—we aren't transported directly into Harry's head, as we would be in first person narration, but we tend to follow events from his perspective) whereas an omniscient narrator evokes far greater narrative distance, with its narrator able to speak about the thoughts and perspectives of all the characters within the story.
This particular story, however, feels like a hybrid between the two: Hemingway's narrator does seem to be tied to Krebs; it is only his internal life that the reader can access, and the perspectives of other characters can only be hinted at through dialogue and action (such as his mother's crying). However, the narration itself takes place at an extraordinary distance, uncommon to third person limited, with a detached objectivity that is more reminiscent of what you would find in third person omniscient. In that sense, this story eludes easy classification, as it incorporates aspects of both third person limited and third person omniscient without clearly fitting into either one.