@Octavious:
"After the touchdown some other chap walks on to the field and kicks the ball between two sticks a few yards away, scoring an extra point. Why? This is the most pointless things I have ever seen in sport. It's so easy it's only ever missed once in a blue moon. What's it for?"
Short answer:
Because the Extra Point (or Point After Touchdown, or PAT, if I wanted to be REALLY anal about it) is worth 1 point...
Which you can go for as a near-sure thing, OR take the chance of going for a 2-Point Conversion, which is accomplished by a pass or run into the endzone from the same spot...
THAT is naturally harder, and only completed about 1/3 of the time, or so--1/2 of the time for a very good team--so it's a bigger risk, BUT can mean the difference between losing a game by one or tying, or else tying the game or winning.
Longer, History-oriented answer:
The reason?
A Field Goal was originally worth 6

, and a Touchdown 3.
THEN some guy figured out "Hey, it's actually HARDER to a TD than a FG, so the point values should be switched, as it's proportional."
And they are.
A TD is worth 6, a FG is considered "half" as hard, or so--since you're not going the whole length of the field anymore to score points, you're stopping and kicking--so half of 6 is 3.
The PAT was THEN added as a method to further encourage TDS...THAT WAY, a TD would be worth EVEN MORE than a FG; as it stood, 6 was 2x > 3, so a PAT made a TD worth slightly more than 2 FGs, thus encouraging the TDs that have so fueled the game's success...
As while a last-second FG can be exciting, just watching a team drive only 3/4 of the way and kick is less exciting than going all the way (and if you doubt that logic, ask any girlfriend which they'd prefer, 3/4ths the effort, or "going all the way."
;)
THEN, in the 1960s, the NFL, then at 12-14 teams or so, got competition from the AFL, a rival league, where many of the most prestigious teams in the NFL today started:
New England's Patriots (obviously in the SB this year...at that time, they were the "Boston" Patriots...)
Oakland/Los Angeles' Raiders (who were good until Al Davis effectively went senile...)
Miami's Dolphins and Denver's Broncos (5 SB trips and 2 wins apiece...)
And others.
WHY did this league survive?
One answer was, a VERY wide offensive game...THEY were the first to implement the idea of the 2-Point conversion.
So, the two leagues merged, the NFL adn AFL, and 30 years later, in the good old 1990s, someone at the league office said "Hey, ratings are good, but what would make this offense-driven league even MORE exciting? More points, so let's bring back the 2-point conversion!)
And so it has been:
1 point for a PAT
2 for a 2-Point Conversion OR Safety by the defensive (Tackling a player in his OWN endzone)
3 for a FG
6 for a TD
"But wait!" those logically-inclined might be asking, "why not just make a TD 7

and assure the 7 UNLESS they go for a 2-Point Conversion, and if they miss it, THEN they only earn 6? THEN you save the trouble of making us watch the kicker for all of two minutes!"
To which the obvious answers, are, of course:
1. Well, sometimes...well, they DO miss, sometimes, and their embarrassment's fun...
2. I thought Europeans was into kickers and kicking balls around?
3. Tevye's answer works best here--
"TRADITION!"
And there you have it!
The history of the NFL scoring system, why everything is what it's worth...
And waaaaaay more than you needed to know on the matter! ;)