The point of view used in "A Sound of Thunder" is third-person limited. This means that the narrator is not a participant in the events of the story; the narrator does not refer to themselves using the first-person pronoun "I" or "we." The term "limited" means that the narrator can only report the thoughts and feelings of one character in the story; here, that character is Eckels, the hunter who goes back in time to kill a Tyrannosaurus Rex and totally chickens out.

One example of this is when the narrator tells us that Eckels "had weighed the evidence and [it] was his considered opinion [that the dinosaur could not be killed]. The rifle in his hands seemed a cap gun" to him. If the narrator could not report on the thoughts and feelings of this character, then they would be unable to tell us something that Eckels only thinks and does not say aloud. That his rifle feels like a mere cap gun in the face of this huge monster would be a detail we could not know.

The narrator also tells us how Eckels thinks and feels after the men return to the present time. Eckels realizes that he stepped on a butterfly when he went off the path in the past, and "his mind whirled. It couldn't change things. Killing one butterfly couldn't be that important! Could it?" This is another example of the narrator revealing Eckels thoughts, describing things he does not say aloud.

The point of view is third person limited from the perspective of Eckels.

When we talk about point of view, we usually refer to first person or third person.  First person point of view has a narrator who talks directly to you, and uses the first person. You can tell because he or she will use the words “I” and “my.”  These are first person pronouns. 

A third person narrator uses the character’s name and third person pronouns like “he” or “she” to describe the person telling the story.  Within third person point of view narration there are two kinds: limited and omniscient.  An omniscient narrator knows what all of the characters are thinking and feeling, and a limited narrator follows just one.

This story is told from a third person limited perspective, with Eckels as the narrator.  You can tell this right away, by Eckels’s reaction to the sign. 

Warm phlegm gathered in Eckels' throat; he swallowed and pushed it down. The muscles around his mouth formed a smile as he put his hand slowly out upon the air, and in that hand waved a check for ten thousand dollars to the man behind the desk.

Eckels is a customer at the time travel office.  He is coming to buy a ride in the time machine to shoot dinosaurs.  Why he wants to do this I do not know, but he seems a little nervous about it.  I would be too.  He also seems to be fairly wealthy.  It is expensive!

Throughout the story, we know what Eckels is thinking and only Eckels (unless another character is talking and tells us what he is thinking).  This is useful because it increases the suspense.  We learn about time travel and the butterfly effect just like Eckels.

“…Stay on the Path. Don't go off it. I repeat. Don't go off. For any reason! If you fall off, there's a penalty. And don't shoot any animal we don't okay."

"Why?" asked Eckels.

Eckels will learn why.  Oh boy, will he learn why.  However, he does not know why and neither does the reader, because the story is told from a third person limited perspective. 

If it were third person omniscient, I think Mr. Travis would be thinking, “This idiot is going to alter the course of history by stepping off the path!  Why don’t they ever listen?  We really should screen these people better.”  I imagine it would be something like that.

What point of view is "A Sound of Thunder" written in, and why is it important?

When we think of point of view in terms of literature there are three different types that are used mainly by authors: first person, the omniscient point of view (all-knowing) and third person limited. The third person limited point of view is interesting because we still have an exterior narrator who is outside of the story looking in on the action, but this narrator chooses to tell us the story from the point of view of one character alone. The narrator is still exterior to the tale, so it is not first person point of view, but this narrator focusses on one character alone.

It is clear from the very first paragraph then that the third person limited point of view is the one that Bradbury uses in this excellent short story. Consider the first paragraph:

The sign on the wall seemed to quaver under a film of sliding warm water. Eckels felt his eyelids blink over his stare, and the sign burned in this momentary darkness... A warm phlegm gathered in Eckels's throat; he swallowed and pushed it down.

Note how the story is narrated in the third person, but we are still focussing on one character alone. The benefits of this approach is that we are able to remain exterior observers to the tale as we follow one character and we don't know what the other characters' are thinking and feeling, except through their words. This is crucial in this story as we are never aware until the end how serious Travis is in terms of the punishment he will visit on anyone who does change the future. Hearing the "sound of thunder" from Eckels's perspective alone at the end of the tale seems to emphasise the horror of his untimely end.