A cover story was a made-up explanation for one's presence in a location where one was otherwise not supposed to be, or for an operation whose true purposes were to remain a secret.
In 2063, Deanna Troi told Zefram Cochrane her cover story, which he didn't believe. (Star Trek: First Contact)
In 2377, Chell speculated that the comas which several ex-Maquis USS Voyager crewmembers had lapsed into were in reality a front for orders from Starfleet Command to neutralize the Maquis threat on Voyager. B'Elanna Torres found the theory to be ludicrous. (VOY: "Repression")