From The New York Times:
Mr. Carlsen, who turns 19 on Nov. 30, is only the seventh No. 1-ranked player since the ranking system began in 1970. Garry Kasparov, the Russian former world champion, became No. 1 in January 1984, when he was 20 years and 9 months old. He held the spot for 18 months, lost it, and then regained it and held it for 20 consecutive years before retiring in March 2005.
Rankings are based on cumulative performances, measured by something called a rating. Mr. Carlsen’s rating is now 2,806, and Mr. Topalov’s is 2,805. Mr. Anand, 39, the current world champion, finished in a tie for fourth in Moscow and is now No. 3, with a rating of 2,790.
Although he is the world's highest rated player, Carlsen can not become World Champion for a few years. In April, Veselin Topalov of Bulgaria and defending champion Viswanathan Anand of India will play a world championship match of several games in Sofia, Bulgaria to determine the next World Champion. Carlsen is expected by many to become World Champion in the next few years.