Team Fortress 2 is about a group of average, everyday, working-class mercenaries. Crack that manual open, though, and it's a different story. You've been hired to mop the floor with their asses.' For the average player, it really doesn't get any more complicated than that.
Said plot, in all of its glory, is 'The other side is the enemy, and vice versa. A sequel to the classic Half-Life 1 mod Team Fortress Classic, itself based on Team Fortress (a popular mod for Quake), Team Fortress 2 has the kind of story a multiplayer-only shooter should have: interesting settings, awesome character classes that each have a distinct personality and can be easily recognized just by their silhouette, and an Excuse Plot that stays All There in the Manual.