The extra point is among the oldest parts of the game of gridiron football and dates to its soccer roots. In its earliest days, scoring a touchdown was not the primary objective but a means of getting a free kick at the goal (hence why the name "try," more commonly associated with rugby today, is still in American football rule books), and thus while a field goal would be 5 points, a touchdown would only be one point and the conversion would be worth four (for a total of five). By the start of the 20th century, touchdowns had become more important and the roles of touchdown and kick were reversed. By this time the point value for the after-touchdown kick had reduced to its current one-point value while the touchdown was now worth five. (This later increased to six points in American football in 1912 and in Canadian football in 1956.)
If two extra points are needed or desired, a two-point conversion (touchdown conversion) try may be attempted by running or passing from scrimmage instead of the extra point kick. A successful touchdown conversion brings the score's total to eight.
In the National Football League, the scrimmage for point after touchdown takes place from the two-yard line. In American high school and college football, it is from the three-yard line. In Canadian football it is from the five-yard line. The game clock does not run during an extra-point attempt, except for some rare circumstances at the high-school level.
In the NFL and American high school football (in most states), the play is over once either the attempt fails or the defense takes possession. In many other levels of football, including the Canadian Football League and American college football, the play continues until the ball is otherwise dead. This allows the defense to recover the ball to return it to the opponent's end zone for two points. Two states, Texas and Massachusetts, play high school football under NCAA rules and thus allow the defense to score on an extra point attempt.
In the NFL, the attempt for extra point(s) is required after a touchdown scored during the regulation (i.e., not overtime), because points are used for some tiebreakers in the standings. Rarely, this can result in such an attempt having to be made at the end of the game when it cannot change the outcome of the game. If the game is in sudden death overtime, the extra-point attempt is omitted if the winning score is a touchdown. In American high school and college football, it's likewise omitted following a touchdown on the game's final play if six points were enough to win or if the scoring team was already ahead.
The World Football League and XFL eliminated the extra-point kick in their short lives and only allowed a one-point scrimmage play, although the XFL later implemented a variable system that allowed increasing point values for increasing the distance to the end zone on the attempt for its playoffs.