The story was indeed fishy, which means that it smelt suspicious and was not quite believable or sounded far-fetched. Every person that Jerome and George encountered in the tap room of the inn that afternoon claimed to have caught the trout which was displayed in a glass case. It was an exceptional specimen because it was huge. Jerome and George were first told about its capture by two gentlemen who told different stories about how they had caught the remarkable trout. They became suspicious and realized that one of the two men, or both, must have been lying.
When a third gentleman arrived, George asked him to divulge to them how he had managed to bag such a magnificent specimen. After expressing surprise at the question and asking who had informed them, the man gave them a rendition of how fortunate he had been in capturing the trout when they told him that they just assumed that he must have been the one who had caught it. At this point they were convinced that everyone had been lying.
The two were obviously intrigued and wanted to establish the truth about the fish and, when the landlord arrived, they enquired about it. He laughed and mocked the three men who had previously claimed that they were the ones who had bagged it. He sarcastically commented that if they were the ones who had captured it, why would they allow him to display it in his parlour? He then divulged what his two guests believed to be the truth. He sounded quite convincing and added a little detail to give the story some flavour.
However, once he had left, the men sat staring at the fish and George became so excited that he wanted to take a better look at the wondrous specimen. The chair on which he stood slipped, though, and in an attempt to save himself, he wildly grabbed at the case, bringing it crashing down. When the two looked at the trout, they saw that it had splintered into many different pieces. The trout had actually been a fake made out of plaster of Paris (gypsum)—the material used to hold bones together or to create models. This proved that everyone had been lying, including the believable landlord.
The story mocks a human foible. Once an achievement can be claimed and there is no evidence or witnesses to question our veracity, it becomes easy for some of us to take credit where no credit is due, either to boost our egos or for some other obscure reason.
Jerome K. Jerome cleverly plays on the fact that we are quite naive and can be easily misled, as when he states that the landlord was an "honest old fellow" and that "he told us the real history of the fish." Our two characters had been taken for a ride and would never have discovered the real truth if it were not for George's accident.