The official strike zone is the area over home plate from the midpoint between a batter's shoulders and the top of the uniform pants -- when the batter is in his stance and prepared to swing at a pitched ball -- and a point just below the kneecap. In order to get a strike call, part of the ball must cross over part of home plate while in the aforementioned area.
Strikes and balls are called by the home-plate umpire after every pitch has passed the batter, unless the batter makes contact with the baseball (in which case the pitch is automatically a strike).
The vertical specifications of the strike zone have been altered several times during the history of baseball, with the current version being implemented in 1996.
Past strike zones
Note: The box outlined above delineates the borders of the Major League strike zone.