The best way to answer this question is to analyze how the narrator describes Simon Wheeler. In the short story "The Celebrated Jumping Frog of Calaveras County" by Mark Twain, the narrator visits Wheeler to ask about a man named Leonidas W. Smiley. Wheeler instead tells him about Jim Smiley, an eccentric individual with a penchant for betting on animals. The climax of the tall tale is a description of a jumping contest between Smiley's celebrated frog and a random rival, in which Smiley's opponent fills the frog's belly full of quail shot.
At the beginning of the story, the narrator describes Wheeler as good-natured and garrulous. According to the Merriam-Webster Dictionary, "garrulous" means "given to prosy, rambling, or tedious loquacity: pointlessly or annoyingly talkative." In other words, Wheeler is pleasant and friendly but talks too much. The narrator describes Wheeler as having "an expression of winning gentleness and simplicity upon his tranquil countenance." "Winning" when used to describe a person means "tending to please or delight." So we see that Wheeler is gentle, pleasing, and peaceful.
The narrator then describes Wheeler backing him into a corner and blockading him with a chair, as if he is afraid that his audience will escape. Wheeler then tells the long story of Jim Smiley in a monotone without interruption. At the end of the tale about the jumping frog, Wheeler button-holes the narrator and begins to start another story, but the narrator manages to leave. To "button-hole," when used as a verb in this context, means "to detain in conversation by or as if by holding on to the outer garments of" the conversational partner. In other words, Wheeler metaphorically tries to grab the narrator's clothes to keep him from getting away. Finally, while the narrator is leaving, he describes Wheeler as sociable.
With these clues, we can attempt to answer your question. It is evident that Wheeler does not merely like to hear himself talk, because if that were true, he would not need an audience. Wheeler, however, is good-natured, winning, and sociable, so he appreciates and values the company of others. It is not evident, though, that he thinks he is imparting something important or educational to his listener. Instead, it seems that his intention is to entertain, and his hope is that if his stories are entertaining enough, his listener will remain longer and keep him company. The correct answer, then, is neither of the options that you have presented, but rather that Wheeler talks so much and tells his stories to be sociable and to entertain his visitor.
Wheeler is playing Twain's persona, the first person narrator, for a fool. It's also clear that Wheeler enjoys his own joke, so it is not inaccurate to say that he "likes to hear himself talk." However, his story should be understood ironically. Wheeler seems dead serious about the story he tells about Smiley. It is, in fact, part of an elaborate ruse he plays on the narrator, who takes it...
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all at face value. For the educated Easterner, Wheeler seems to conform to Eastern stereotypes about eccentric Western "characters."
On the other hand, Wheeler does take a certain pleasure in the elaborateness of his story, and part of Twain's point in writing the story is to celebrate Wheeler's inventiveness and the fun of tall tales in general. In a way, the trick played on Smiley's frog is not unlike the trick Wheeler is playing on the narrator. They are both pranks of a kind. Both suggest that such stories are a confidence game meant to victimize the listener. The narrator has the sense to recognize this by the end of the story, managing to escape when Wheeler is called away briefly. It is left to the reader to determine if Twain himself has been playing the same sort of trick on him or her that Wheeler has played on Twain.
In the exposition of his humorous story, Mark Twain as narrator observes that the fat, bald-headed and simple Simon Wheeler is sincere in his recounting of his tall tales,
...all through the interminable narrative there ran a vein of impressive earnestness and sincerity, which showed me plainly that, so far from his imagining that there was anything ridiculous or funny about his story, he regarded it as a really important matter.
However, since it is later revealed that the narrator has been the butt of a practical joke since there is really no Leonidas W. Smiley, when Wheeler notes that the visitor is from the East, he has some fun with his pedantic new guest by feigning sincerity and naivete regarding the absurdity of his tale. Thus, with his exaggerated story--"you never see a frog so modest and straightfor'ard as he was"--and local dialect and parodic names of frogs such as Daniel Webster, Wheeler creates a burlesque of his "lofty" narrator who feels he must politely tolerate Wheeler. In affirming this use of the burlesque by Wheeler, critic Paul Schmidt in his essay "The Deadpan on Simon Wheeler," writes,
Contrary to "Mark Twain's" picture of him as "far from imagining that there was anything ridiculous or funny about his story," Wheeler is fully aware that his manner is comic and that he is clowning when he treats the frog in his story like a prima donna. He poses as stupid in order to ridicule what his genteel auditor, "Mark Twain," projects on the vernacular Westerner, in order to show how ridiculously inappropriate the stereotype of the western barbarian is and how wrong the genteel values are which led to its imposition.
Therefore, Wheeler's intention is not to merely weave a tall tale, but to provide a witty Western version of "Mark Twain's" pompous Eastern language that creates a burlesque of the Easterner's " affected speech and insincere manners. Indeed, Simon Wheeler hopes to instruct his listener.