"A Sound of Thunder" describes the misadventure of a rich big-game hunter, Eckels, who has paid for a "time safari" - a trip to the distant past using a time machine, in order to hunt animals that are extinct, in this case dinosaurs. A considerable amount of the story is devoted to exposition and argument from the safari guides to the somewhat hapless Eckels, repeatedly emphasizing how delicate an affair time travel is, and the potential for any errors to be disastrous not just for themselves but for the reality they expect to return to when they get back in the time machine. 

When faced with the tyrannosaur he has arranged to kill, Eckels turns unexpectedly cowardly and falls off the safari's designated path; this was one of the things he was explicitly instructed not to do. At the time he is unaware that he has accidentally killed a butterfly. 

When the group returns to 2055, it is not immediately apparent that things have changed;

The room was there as they had left it. But not the same as they had left it. The same man sat behind the same desk. But the same man did not quite sit behind the same desk.

Two additional, specific details are provided; the wording on the Time Safari sign has changed to resemble a phonetic or illiterate form of English, and a different president has been elected. A general change in the setting is an unspecified, faint chemical smell in the air, perhaps included by the author to signify that the changes are both obvious and subtle, and that we don't always necessarily acknowledge all of the elements that compose the settings we are most familiar with.  

The overt message seems to be that this new version of 2055 is worse, specifically because its political and intellectual values have changed or diminished in quality, compared to what the characters expected.