The two most significant and related themes of the story "A Sound of Thunder," are that the existence of everything is connected to the existence of everything else and that human life cannot be isolated from what happens in nature.

While in the past, Time Safari client Eckels panics at the sight of the Tyrannosaurus Rex he has paid to kill, and he steps off the path and onto a butterfly. When the men return to the present after having killed the great dinosaur, they see that the spelling of the Time Safari business sign is completely strange and different, and the man at the desk is "not quite the same man" he was before they left. Eckels drops into a chair and, in examining his boots, realizes that he has stepped on a butterfly.

It fell to the floor, an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time.

Somehow, Eckels stepping on that butterfly changed the course of evolution and natural development and even the fates of human beings living millions of years later. In fact, human relations and lives are so intimately connected to the natural world, even to the long-past world of the dinosaurs, that the death of one insect millions of years ago has changed the outcome of the recent presidential election. Eckels thinks, "Killing one butterfly couldn't be that important! Could it?" The answer, of course, is that it could be and it is that important.

One of the main themes of the story is the dangers of exploiting nature. By making regular hunting expeditions to prehistoric times, Time Safari Inc demonstrate just such an exploitative attitude. They see nature as nothing more than an object that exists for man's personal use. The idea of nature as being intrinsically special, as having a life of its own, simply doesn't occur to them. All the company cares about is making a quick buck.

And how does Time Safari Inc exploit nature? Through developments in technology. Bradbury may not be a Luddite—someone with a knee-jerk fear or distrust of new technology—but here, as elsewhere in his works, he's alive to the dangers of how it can so often be used or, rather, abused.

On paper, the ability to travel through time sounds amazing. Most of us at some point have probably imagined what it would be like to go back in time to places we've only ever read about in history books. But if such technology ever were to become available, then, as the story makes clear, it would be put to less savory ends—used as a means of exploiting the environment and messing around with history, with potentially serious and damaging consequences.

The theme of the story could be summed up as "do sweat the small stuff." Details matter. More importantly, we need to get beyond ourselves and our own pride and realize that the whole world is linked together in delicate and intricate ways. Even our smallest actions can have big consequences, so we shouldn't be reckless.

In this story, Eckels indulges himself with a very expensive trip back in time to the dinosaur age. Despite severe warnings to be extremely careful and to stay on a strictly prescribed path, he steps off in fear and confusion and kills a butterfly. He has realized too late that they shouldn't be there, stating

 "We were fools to come. This is impossible."

When he returns to the present, he realizes that his one mistake in killing the butterfly has had huge repercussions: history has been changed, and a Hitler-like dictator has been elected president.

The most important theme in the story, one that can get lost under our fascination with time travel and the dinosaurs, is that our human pride can lead to our undoing. The same pride or ego—a form of recklessness—that leads humans to think they can safely control time travel can lead us to make reckless decisions with devastating consequences. We do need to live carefully, to sweat the small stuff, to think before we act.

“A Sound of Thunder” is a science fiction story about a man named Eckels who hires a time travel company to take him on a hunting expedition in the age of the dinosaurs.  The theme is that little things can make a big difference.

This story reminds us of an idea called the “Butterfly Effect.”  The Butterfly Effect states that a very small event can have large unintended consequences.  In the story, Ecklels is warned never to step off the path, because they can only hunt animals that are already about to be killed if nature runs its course.

It floats six inches above the earth. Doesn't touch so much as one grass blade, flower, or tree. It's an antigravity metal. Its purpose is to keep you from touching this world of the past in any way.

This little bit of foreshadowing, the insistence that he stay on the path, is directly related to the theme.  When you step off the path, something happens that you do not intend.  You can affect the entire course of the future, just by stepping on a butterfly.

"Not a little thing like that! Not a butterfly!" cried Eckels.

By stepping on the butterfly, Eckels altered the path of history such that the spelling on the sign was changed and a new man was elected president.

We probably won’t go time traveling in our lifetime, but this is still a relevant theme.  Sometimes a little thing can make a big difference.  One small choice, although it may seem minor, can affect not only the course of your future but others as well.