The extra point is a play common to all forms of American football. It is a play immediately following a touchdown and is also sometimes called the "point after" or the "point after touchdown" (PAT).
Both the Canadian Football League and NCAA rulebooks have long, complicated descriptions of the extra point attempt. The best, most-succinct description and summary comes from NFL rulebook:
1. After a touchdown, the scoring team is allowed a try during one scrimmage down. The ball may be spotted anywhere between the inbounds lines, two or more yards from the goal line. The successful conversion counts one point by kick...
The kick has to successfully pass between the upright goalposts in order for it to count and the kicking team be awarded the point.
It's worth pointing out that the rule above specifically states that the ball may be spotted "...anywhere between the inbounds lines, two or more yards from the goal line". There are a few reasons for this:
First, it's saying that the kick itself must occur at or behind the 2-yard line because there is nothing in the rules prohibiting the kicker from taking the snap, running around a bit, and then attempting a drop kick on the play. The kicker simply cannot advance past the 2-yard line (or whatever the current line of scrimmage is) before kicking it -- he has to do it at or behind it. This part of the rule is a relic from the early days of the game when it resembled rugby a lot more and the ball itself was more-round (and when the drop kick, which is still allowed in the current rulebook, was more common).
Secondly, standard practice on a placekick attempt for extra point in today's modern football would place the ball on the two-yard line prior to the snap. The ball is then snapped roughly 7 yards to the rear of the formation, where the holder catches the snap and places it down so the kicker can kick it. This rear placement is done in order to give as much protection as possible to the kicker and holder, making it harder for an opponent to block the kick.
Finally, should the kicking team be penalized during an attempt this particular wording of the rules allows the yardage penalty to be assessed and the extra point then retried from further back. Or more-simply put, if the kicking team gets penalized for something like a false start during the attempt, the line of scrimmage would then be moved back 5 yards from the 2-yard line to the 7-yard line (and the actual placekick would then take place from roughly the 14-yard line as a result).
Football teams at lower levels of play often won't even try to kick the extra point, as they may not have a capable kicker on their roster. Instead they'll opt to try for a two-point conversion. Beyond that level the extra point is a staple of football and often considered a nearly-automatic point. There are numerous things that can go wrong with the play though, such as a botched snap from the long snapper, or the holder failing to hold or properly place the ball so it can be kicked. A missed extra point can often be the difference between a tie game going into overtime and a loss in regulation, so it's still a very important play every time.
Extra points are attempted from the 3-yard line in NCAA or high school, 2-yard line in the NFL, and 5-yard line in the CFL.