The touchback rule only applies to American football. Touchbacks occur in the end zone and result in the offensive team beginning play from their 20 yard line. The NFL rulebook explains that a touchback occurs when the ball's momentum, created by the opponent, carries it onto or inside the goal line, where it becomes "dead." The only exceptions to this are missed field goals and touchdowns.
In American football -- especially at the college and professional levels -- the player executing the kickoff often kicks the ball into the opponent's end zone. If the returner catches it, he can either attempt to run the ball out of the end zone or kneel down and give himself up. If he kneels, it is a touchback, and his team gets the ball at their 20 yard line. He can also let the ball go through the end zone. Once the ball goes out of bounds in the end zone, it is a touchback.
In the NFL, a punted ball does not have to enter the end zone for a touchback to occur, though this is often the case. A player on the punting team who attempts to down the ball before it crosses the plane of the goal line must keep both feet outside the goal line. A member of the punting team who touches the ball with a foot on or inside the goal line, even though the ball may not have entered the end zone, causes a touchback. A ball that is touched by a punt-coverage player that then rolls or bounces into the end zone is also a touchback.
Touchbacks can occur from fumbles and interceptions. If the offense fumbles into the opponent's end zone, a defensive recovery in the end zone results in a touchback. It is also a touchback if the offense fumbles and the ball goes out of bounds in the opponent's end zone. Additionally, if a defensive player intercepts the ball in the end zone and is tackled inside the goal line (or kneels and gives himself up) it is a touchback, and the offense will take over from the 20 yard line.
Differences with Safeties
Safeties and touchbacks both occur in the end zone, but a safety is a defensive play and rewards the defense with two points for their team. Safeties occur when the ball carrier is outside his own end zone and decides to enter it. If he is tackled behind the goal line, it is a safety. If the offense fumbles into their own end zone and the recovering offensive player is downed in the end zone, it is also a safety. The team that concedes the safety must then kick off to their opponent.