Diplomacy (presently trademarked by Hasbro/Wizards of the Coast) is a strategy boardgame invented by earthdweller Alan Calhamer in the middle of the 20th Century. Its mechanics are deceptively simple and, in many cases, fairly routinized. The soul of the game lies in looking into the minds of one's foes and there finding truth. And, of course, manipulating it to serve one's own ends.
The game is played out on a map of Europe representative of the geopolitical situation in the 19th and early 20th centuries. Each player takes the role of one great power (Austria, England, France, Germany, Italy, Russia, or Turkey, symbolized in that order above by tasteful and partially accurate flag imagery). The object of the game is to control just over half of the "supply centers" on the game map. The game involves periods of negotiation followed by periods of order writing. These alternate until the game is concluded--often many hours after it began. The game is also played by mail and email. The game's popularity has spawned numerous variants.
More complete information on the game is available at The Diplomatic Pouch, the Web centerpiece of the North American Diplomacy hobby. The Pouch has information on upcoming events, online play, and an extensive library of articles which will make you a better player - or at least help you appreciate the skill of the person who keeps wiping the board with you.
A final resource is Board Game Geeks, which has extensive information on Diplomacy and many, many other games.