L4D2 is mainly an on-line game that you play with other players. Even though it has a single player mode, they are really just campaign maps.
As for the story line, that's it. Your dropped into a zone with a ton of zombies and you have to fight your way out. The games play homage to movies like Dawn of the Dead, etc.
Playing single player gets boring. It's when you go online and play with other people that you discover the real fun and joy of the game.