What does the sign say at the beginning of the story in "A Sound of Thunder"?
The sign tells customers that they can go to any time period and shoot any animal.
The story takes place at some point in the future where the technology exists to travel through time. In addition to traveling through time, they apparently have developed some pretty sophisticated weapons. They can shoot animals like dinosaurs.
People have used this technology for what may seem like the frivolous practice of time travel safaris. Time Safari, Inc. has a sign at its entrance to greet customers. Eckels seems fascinated by it when he first comes in.
TIME SAFARI, INC. SAFARIS TO ANY YEAR IN THE PAST.
YOU NAME THE ANIMAL. WE TAKE YOU THERE. YOU SHOOT IT
Apparently the technology to travel through time and shoot dinosaurs is common enough and inexpensive enough that it can be used for commercial purposes. However, this activity is government regulated. There is heavy regulation because going back in time can change the future.
“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, … thus destroying an important link in a growing species.”
Eckels hired Time Safari to take him back to the time of the dinosaurs to shoot a Tyrannosaurus Rex. He was a big game hunter, and wanted a more challenging hunt. He paid ten thousand dollars to hunt the T-rex. Yet when he was face to face with the dinosaur, he panicked. It seemed too big and scary to actually hit.
It turns out that stepping off the path does change the future. Eckels gets so frightened by his experience that he accidentally kills a butterfly, and when he returns the lettering on the sign has changed just enough that we can tell that the future was altered. A different man is president. It is the butterfly effect.