Campaign -- RPG or Wargame
Clarifying on the other write-ups give, the term "campaign" is used in reference to a long-term tabletop role-playing game or miniatures wargame. Generally, campaigns involve regular meetings of the players and an ongoing story.
This usage of the term "campaign" evolved from the fact that RPGs came out of the miniatures wargaming industry. The originator company of Dungeons and Dragons, the first RPG, was firstly a fantasy miniatures wargaming group (TSR, Inc. = Tactical Studies Review.)
This is also part of the reason that gamers often think of combat as the centralmost part of the RPG experience and why the rules for combat are generally exacting and detailed. While trying to avoid the problem of "'Bang! bang! I shot you you're dead!' 'No, I'm not, you missed!'", the game is also reaching back to its roots. The lest exacting a game's combat system, it seems the further removed from miniature wargaming.