A slightly misleading title though, he's not a world champion but number one in the rankings, which is not the same. Still fascinating.
http://en.wikipedia.org/wiki/World_Chess_Championship
... is that nobody has ever become world champion at a younger age than their twenties.
Being a chess idiot, I don't really know why this has been true, but I assume it's simply a matter of practice: that it takes time to get good enough at chess to usefully train against grandmasters, and then it takes time with the grandmasters before you can dominate at grandmaster-level chess, which my chessmaster friends have told me is almost like a different game, one which they can follow with great excitement but not necessarily understand well enough to play.
The book "Talent Is Overrated" cites some interesting studies on chess players that support the idea that this is probably the main factor. Basically a combination of improved training methods, long hours of deliberate practice, and starting at as young an age as possible. There isn't much in the article that would lead me to think otherwise. The comparison to Mozart is interesting as the book goes into much detail citing evidence how much of Mozart's "talent" was due to his father's efforts to deliberately train him to become a great musician.
For those who are interested, Carlsen has a blog: http://www.arcticsec.no/index.php?button=blog
If you're a purist, you probably believe that one can only become world champion by defeating the title holder in a head-to-head match consisting of of many (12-24 or more) games. That's how it was done from 1886-1993, and I think most chess players (myself included) prefer that format. But Topalov is technically recognized by FIDE as a World Champion.
More here if anybody cares: http://en.wikipedia.org/wiki/World_Chess_Championship