The answer to this question can be found in the text of the story. Jim Smiley has trained his frog Dan'l Webster to be a good jumper. According to Simon Wheeler, Smiley did nothing for three months but sit in his back yard and train his frog to jump. His plan was to get people, especially strangers, to bet on their frog against his. A certain stranger looks like a good prospect when he says that he doesn't see anything special about Dan'l Webster.
“Maybe you don't,” Smiley says. “Maybe you understand frogs, and maybe you don't understand 'em; maybe you've had experience, and maybe you ain't only a amature, as it were. Anyways, I've got my opinion, and I'll risk forty dollars that he can outjump any frog in Calaveras county.”
So each man agrees to put up forty dollars, which was a big sum of money in those days. But the stranger doesn't have a frog to compete with Smiley's, so Smiley went to the swamp and caught another frog. But he made the mistake of leaving Dan'l Webster in the care of the stranger. This man was not the sucker Smiley took him for. The stranger fills Smiley's frog full of quail shot, and poor Dan'l Webster cannot even lift himself off the ground when the contest begins. He can only shrug his shoulders "like a Frenchman." (This is called a Gallic shrug.)
Further proof that the bet is for forty dollars is to be seen in the following passage:
And so the feller took the box [with Dan'l Webster in it], and put up his forty dollars along with Smiley's, and set down to wait.
What makes Mark Twain's story so amusing is not so much what happens as the way Simon Wheeler tells it. As stated in the enotes Summary in the Study Guide for "The Celebrated Jumping Frog of Calavaras County":
The repetitions, the grammatical errors, the misspellings to indicate accent, and the wary rejoinders have a seamlessness about them which gives them an air of authenticity, of improvisational vivacity, which is part of Twain’s charm as a comic writer.