The phrase "engrossing story" means a story that completely captures and holds your attention, making it difficult for you to look away or stop reading. Full definition
This hugely entertaining documentary tells the surprisingly engrossing story of a beloved cable channel in Los Angeles. (rottentomatoes.com)
When the game is good though, it can be a dark but engrossing story with a pretentious atmosphere that is its own and filled with some clever writing. (consolealliance.com)
NYPD Blue is telling a tough, engrossing story about several fascinating characters... Chief among them is the grimly determined but not humorless Kelly, played by David Caruso with an irresistibly cool, understated intensity. (metacritic.com)