A wargame, generally, is a type of strategy game which realistically simulates warfare. A professional wargame, specifically, is a wargame that is used by military organizations to train officers in tactical and strategic decision-making, to test new tactics and strategies, or to predict trends in future conflicts. This is in contrast to recreational wargames, which are designed for fun and competition.
A wargame at the US Naval Postgraduate School (June 2018).
A reconstruction of the wargame developed in 1824 by Reisswitz
The Navy Electronic Warfare Simulator (1958).
A wargame at the US Naval War College. This photo was taken in the 1950s, but strongly resembles the wargames played in the 1930s.
A wargame is a strategy game in which two or more players command opposing armed forces in a simulation of an armed conflict. Wargaming may be played for recreation, to train military officers in the art of strategic thinking, or to study the nature of potential conflicts. Many wargames re-create specific historic battles, and can cover either whole wars, or any campaigns, battles, or lower-level engagements within them. Many simulate land combat, but there are wargames for naval and air combat, as well.
A recreational wargame (Here I Stand) in play at CSW Expo 2009
Bolt Action, a miniature wargame set during World War 2
A game of Julius Caesar from Columbia Games shows how a player may only know the strength and unit type of their own forces, creating a fog of war element that does not exist in most tabletop wargames.
The US Navy Electronic Warfare Simulator (1958)