Explain why it is so important that the hunters stay on the path in "A Sound of Thunder."
In "A Sound of Thunder," hunters time travel. When they travel back in time, the hunters must be extremely careful not to alter anything at all that exists in the previous time in which they insert themselves. Even the slightest alteration can disrupt history and the environment.
As Eckels travels back in time, Mr. Travis, the Time Safari guide, explains the importance of not causing any changes in the environment:
The stomp of your foot, on one mouse, could start an earthquake, the effects of which could shake our earth and destinies down through Time, to their very foundations.
When Eckels and his guides Travis and Lesperance arrive in the pre-historic age, Lesperance reminds Eckels not to shoot until he and Eckels give him the word. Travis adds, "Stay on the Path."
Unfortunately, Eckels is too nonchalant about both warnings. He becomes frightened when he sees the Tyrannosaurus Rex, and he slips off the gravity path on which he was strictly told to stay. This slip has devastating results, altering history in many ways.
The Path is an antigravity metal walkway that prevents the hunters, who are engaged in a time-traveling safari to the Cretaceous period, from interacting with the environment in unintentionally destructive ways, such as by stepping on an organism. Because they don't know exactly what effects their actions will have on the future, they want to minimize their influence on the past outside of the animals they intend to hunt.
It is extremely important that the hunters stay on the Path, because this is both a means of minimizing unintentional contact and alteration with the past, and also because it functions as a very clear metaphor for the story; by staying on the Path, one is doing things "right", and straying from the Path implies deviation, chaos and destruction.
As is evidenced at the end of the story, Eckers strayed from the path, crushing a butterfly, and altering the course of history such that English is written differently and a different president is elected when he returns to his own time.