An imaginary line crossing the field which both offensive and defensive players cannot cross until the football is snapped and the play has started. It is also the location where the ball is spotted after running a play or being assessed a penalty.
There are actually two lines of scrimmage in a football game: one for the offense and one for the defense. The difference between the two lines is approximately the length of a football and is referred to as the "neutral zone". Only the center is allowed to have any part of his body in the neutral zone, and the offensive team must have a minimum number of players on the offensive line of scrimmage.
For example, in the NFL there must be seven players on the line of scrimmage, of which two must be eligible receivers. All other players must line up at least one yard back from the line of scrimmage before the ball is snapped.