The phrase "jumping the shark" began as the expression of a single person's opinion as to where the once extremely popular American television show, "Happy Days," began a permanent decline away from its peak until the moment it ended.
In this show, a major character became involved in a water-skiing race. A shark in a netted area of the ocean was to be jumped over as the tiebreaker for the race. This was seen by many as completely ridiculous, and a vivid sign of the declining creativity of the writers of the show. When shows become fully mature, their story lines tend to have already exhausted the best material, leaving second-rate material until the show mercifully comes to an end.
Example: "I think that ____ jumped the shark when..."
Just replace ____ with a given television show, and the idiom is being used correctly.
Rarely, some television shows are considered to have never declined, and maintained a high level of quality right until their final conclusions.