This is one of those fantastic phrases you hear but you may not realize what exactly it means. Jumping the Shark is a reference to the downhill spiral that a website, fashion, television show, etc. takes after reaching great popularity. The term was officially solidified back in 1997, when a site with that name was built: Jump the Shark.
The phrase is a metaphor in reference to Arthur “Fonzie” Fonzarelli jumping a shark on waterskis in an episode of the long-running television series Happy Days. That episode is widely identified as the television series' tipping point in popularity in 1977. Wikipedia states the metaphor was penned by a college room mate of the guy that started the Jump the Shark website.