The Butterfly Effect theme is the idea that a small event can have large effects. It is the idea that “the slightest change in the initial conditions of a chaotic system can accumulate in the long run into an enormous effect” (enotes, butterfly effect).
The famous event from the story is when Eckels, the time travel safari customer, steps on a butterfly. At first, Eckels has a hard time believing that straying off the path is so serious.
"We don't want to change the Future. We don't belong here in the Past. The government doesn't like us here. We have to pay big graft to keep our franchise. A Time Machine is finicky business. Not knowing it, we might kill an important animal, a small bird, a roach, a flower even, thus destroying an important link in a growing species." (see last link).
Even when he notices a dead butterfly on the bottom of his shoe, he cannot bring himself to accept the idea that its death could have changed anything (enotes summary).
An example of this is the end of the story when they realize that there is a different president, and the spelling on the sign has changed. A little change, stepping on a butterfly, can change the course of history.