What is a positional game in chess?
Every position has both positional ("theory") aspects and tactical aspects.

Positional aspects would include the various imbalances in the position:  pawn structure, space, center control, knights-vs-bishops, and pretty much anything else that would generally fall under the category "theory".

Tactical aspects are just what they sound like:  tactics.  I move here, he moves here, and in 4 moves I win his bishop.



A positional game is one that is primarily dominated by positional aspects.  Of course, every game has aspects of both, but in positional games the theory is much more pronounced.  I hear the term "positional game" especially often in conjunction with a closed center - a game in which pawns occupy the center, so attacks have to be mounted on the flanks (sides of the board), usually with pawns rather than pieces.  These games tend to be slower and less intense; it is not uncommon for a player to spend half-a-dozen moves or more moving his knight to its optimal position before pushing a pawn one square.  Because of this, many players consider positional/closed-center games boring.

"Positional game" may also refer to a game where an early endgame was reached, causing most of the game to be dominated by endgame theory.



Tactical games, on the other hand, are dominated by tactics.  For example, see the Fried Liver Attack or the Danish Gambit, which always lead to very tactical games.