Shoot their asses off.' It really doesn't get any more complicated than that. The Excuse Plot, in its entirety, is 'The other side is the enemy.
The above paragraph, quoted from the official website, is literally the extent of the official in-game story (although several special events have started to flesh out the characters, with more to undoubtedly come). Team Fortress 2 has exactly the kind of story elements a multiplayer-only shooter should have: interesting settings, awesome character classes, and an Excuse Plot that stays All There in the Manual. Note: If you're looking for Team Fortress Classic, go here.