Changing anything but what they came there for will trigger the Butterfly Effect.
The Butterfly Effect describes unexpected consequences from a minor event. When Eckels steps on the butterfly, he accidentally changed the course of the future. This is an example of the Butterfly Effect. He only killed one tiny butterfly, but that butterfly affected millions of other events to the point that the future changed.
Eckels hires Time Safari, Inc. to take him back to the age of the dinosaurs so that he can kill one. When he goes back, his guides Travis and Lesperance warn him not to touch anything or step off the path. They tell him that they have carefully selected a dinosaur that would have died anyways in moments, and that is the only thing he can kill. Otherwise, he will set off a shock wave of unintended events.
Crushing certain plants could add up infinitesimally. A little error here would multiply in sixty million years, all out of proportion. Of course maybe our theory is wrong. Maybe Time can’t be changed by us. Or maybe it can be changed only in little subtle ways.
Eckels is a little skeptical, but when he finally sees the dinosaur he is amazed. He can’t bring himself to shoot it, because it seems like something so large is invincible. Travis shoots it for him, disgusted. As they are heading back, they notice that the sign is different. Eckels finds a butterfly on his shoe.
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. Eckels’s mind whirled. It couldn’t change things. Killing one butterfly couldn’t be that important! Could it?
Accidentally stepping on the butterfly created major unintended consequences all right. Somehow the spelling on the sign changed, and the outcome of the election was different. A man whom the others feared has been elected, a move that they worried would produce a dictatorship. One butterfly's death changed the entire future in small ways and large ones.