In gridiron football, the red zone is the area of the field between the 20-yard line and the goal line. The red zone has no official meaning during the process of playing the game and is not generally marked on the field (although some professional stadiums may have special striping for the 20-yard line). The term is mostly for statistical, psychological, and commercial advertising purposes (radio networks have been known to sell sponsorship of the red zone whenever the home team enters it). It is said to be a place where the chances of scoring are statistically higher.
Being closer to the end zone, play while in the red zone involves closer cramping of the offense and defense. The short field of play means safeties have a smaller area to worry about defending, wide receivers do not have to run as far, and passes are not thrown as far. Though the distance to the goal line is less than other parts of the field, with all defenders being crammed into a smaller space and having less room to worry about defending, advancing the ball and ultimately scoring may be more difficult. (This is less of a factor in Canadian football, where the end zones are significantly deeper and wider than the American game.)
For all but the weakest amateur kickers, the red zone is universally within field goal range, assuring that points will be scored on a drive unless the team on offense commits a turnover (either an interception or a lost fumble). As a result, ball control is a greater priority in most red zone situations.
In the "Kansas Playoff" method of settling ties, play is generally confined to the red zone.