On the journey to prehistoric times, Travis warns Eckels of the possible consequences of not following orders to the letter - that there could be dramatic changes in the future. He gives an example of killing a creature not designated in the hunt and how it could have far reaching implications. This foreshadows what is to come.
Unfortunately, Eckels panics at a crucial time of the hunt and flees from the prepared path. It seems an innocuous occurrence, but as we later find out Travis's fury is fully justified. Upon their return, they discover a changed 'future'. As a result of Eckels leaving the path, he has crushed a butterfly under his boot, "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" (final page). To Eckels' horror, he finds that his undisciplined act has in fact made changes to time. For example, language has changed, the result of the presidential election has been altered and even the very air seems to now be tainted.
Eckels is one of the hunters who accompanies the Time Safari group as it travels to prehistoric time to kill a dinosaur. The group leaders, Travis and Lesperance, have done their best to insure that the future will not be impacted by anything the group does in the past. They have constructed a path that everyone must walk on, so as not to disturb the earth or anything lying on it. They have already figured out which animals will be killed by natural causes, so that killing them around the same times will not change any future outcome. In this instance, the Tyrannosaurus rex they have targeted will have been killed by a falling tree anyway. Eckels hears these instructions, questions them, and seems to understand the need to follow the rules. But the sight and sound of the dinosaur are so terrifying to him that he stumbles back to the time machine with hardly any awareness of what he is doing. When the group returns to the future—really, their present day—they see that changes have obviously taken place in their absence. Eckels had stepped off the path and had accidentally killed a butterfly, which is now stuck to the bottom of his shoe. Even this small and seemingly meaningless death has made all the difference. This is a lesson in the intricate weavings of the earth’s environment, showing that every action has a corresponding reaction, and that every little bit of matter counts in some way, even if we cannot see its importance at the time. From this story and others we get the phrase “The Butterfly Effect”: the ramifications of a small act in the past that increase over time to have a greater impact on the future.