A Sound of Thunder is about five Time travelers going to hunt a Tyrannosaurus Rex. This group of travelers walk on the Path to avoid ruining any animals, plants, or history. The Path is an antigravity metal path that guides them to where they shoot the dinosaur. Eckels, one of the travelers, is astonished by the size of Tyrannosaurus Rex and goes back to the Time Machine to hide. On his way back, he accidentally slips off the Path and steps on a piece of mud and kills a butterfly. When the group heads back home, the man behind the desk changes, and the elected president is a different one than before.
I think the story is trying to show that even a small thing can make a big difference. For example, the butterfly changed who became president, a sign’s wording, a person’s job, etc. Also, when one chooses to disobey one’s parent, one may become untrustworthy, and when one is obedient and truthful, one will have a good reputation.