"The Secret Life of Walter Mitty" is told by an uninvolved third person narrator, though that point of view is limited to Walter Mitty. We follow Mitty through his day, and we only get to see or know the things that Mitty himself sees or knows. Now, what's most interesting about this narration is Thurber's use of what NY Times book critic James Wood calls "free indirect style." (You might also have heard the term "implied indirect discourse, which is also a legit name for it.) What this means is that, though the point of view is indeed third person, Walter Mitty's character extends a sort of influence over the narration. The words that are chosen have more to do with Mitty's mindset than they do with objective narration. How's about an example:
"Wrong lane, Mac," said the parking-lot attendant, looking at Mitty closely. "Gee. Yeh," muttered Mitty. He began cautiously to back out of the lane marked "Exit Only." "Leave her sit there," said the attendant. "I'll put her away." Mitty got out of the car. "Hey, better leave the key." "Oh," said Mitty, handing the man the ignition key. The attendant vaulted into the car, backed it up with insolent skill, and put it where it belonged. (7)
Check out the words "vaulted" and "insolent." To Mitty, it seems as though the parking attendant leaps into the car with great ease because, in contrast, Mitty himself is aging and slow. Who thinks that the parking attendant's skill is "insolent"? Mitty, of course. He feels as though the boy is showing off his skill in contrast with Mitty's inability.
The result, in this story, is that the narration puts us on Walter's side. We feel closer to him because we're getting the story through his point of view. Though the narration is, technically, third person, many of the events are filtered through Walter's eyes.