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."