1. the concept that all things in life are interconnected and are dependent upon initial conditions. That is, if there is a small change in the state of one thing in nature, large differences can occur in a later state.

Further, the ending of Bradbury's story serves to explicate the impact of disobedience of the instructions of Time Safari, Inc. For, Eckels's having stepped off the anti-gravity path causes a butterfly to be killed, and he unknowingly brings this butterfly back on to the present on the bottom of his shoe. When he enters the office of the company, he is shocked to see that the sign is markedly changed, 

Sefaris tu any yeer in the past.
Yu naim the animall
We taekyuthair
Yu shoot itt. 

With trepidation, Eckels asks who won the presidential election hoping to hear that Keith is president and nothing has changed, but a man he does not recognize answers, 

"You joking? Who else? Not that fool weakling Keith. Deustscher, of course. We got a man now with iron guts!"

After learning of this profound effect of his mistake, Eckels begs to take this change back, but such cannot happen unless he does not live. Then, he hears "a sound of thunder" as Travis, who has cocked his rifle, shoots Eckels.

In this story, Eckels has gone to the Time Safari company.  He wants to take one of their trips, which involves going back in their time machine and shooting a dinosaur.  He is told by the man at the office that the penalty for disobeying orders from the Safari Guide is a $10,000 fine paid to the company.  It is also possible that the person who breaks the rules will be punished by the government.

The reason for the strict punishments is that they are trying not to change the future while they are back in the past.  The guide's orders are meant to make sure that they do not change the future and so it is really important to obey those instructions.

Here's a quote from early in the story that shows this:

"This is Mr. Travis, your Safari Guide in the Past. He'll tell you what and where to shoot. If he says no shooting, no shooting. If you disobey instructions, there's a stiff penalty of another ten thousand dollars, plus possible government action, on your return."

Eckels is told very early on in the story that Time Safari, Inc. has strict rules.  He is told to sign documents agreeing to the fact too.  If he breaks the rules, there is a stiff monetary penalty.  Once in the machine, Travis continues to stress the importance of staying on the path and only shooting what they are told to shoot.  Eckels asks why there are all of those rules about not doing anything to disturb past events.  Travis explains it with a mouse.  He says that if a single mouse were to die in the past, all of its descendants would then never exist.  The death of a single mouse could potentially wipe out billions of mice in the following years.  That would also have a huge impact on any food chain that depended on the mice.  Time Travel, Inc. doesn't know if small actions like that will actually come true, but they are not willing to risk the potential; therefore, they have harsh penalties in place to deter customers from trying to mess around with past events.