Why Keep Records?
There are many reasons for keeping a record of a chess game. Unless you have a fantastic memory, keeping score of a game is the best way to have the moves available for critique afterward. This is one of the best ways to improve your game, whether the critique is done by you alone, or you with your opponent (better), or you and your opponent along with a third party, perhaps an experienced player (best).
The Chess World
Knowing how to read a game score brings the entire world of chess into your home. There are newspaper columns, chess magazines, and a fantastically huge number of chess books on the market. Chess masters have been writing down their thoughts, analysis, and systems for hundreds of years. This is all open to one who knows how to read chess notation and opaque to one who does not know how.
Chess-playing computers, chess-playing software programs, huge chess databases, and chess Web pages all use chess notation. You're missing out on an awful lot if you don't know how to read chess.
If you ever decide that you want to improve at chess, you will need to know chess notation. Whether you want to get good enough to beat the computer or someone in particular or to gain a national or international title or rating, you simply cannot progress without it. No coach or teacher will be able to do much with you if you don't have game scores to work with, and you won't even be able to scrutinize your own games without this knowledge.
Blindfold chess, and especially simultaneous blindfold chess, can only be accomplished by those who understand chess notation. The chess master, who has no set or board in sight, calls out her moves. The opponent or opponents, who have sets and boards in front of them and can see the game in progress, call out their response.
Win on Time
You win if your opponent runs out of the allotted time before making the prescribed number of moves in a tournament game. The only way to show that this has indeed happened, though, is to have your game score ready along with the clock that shows the time is up. Obviously this cannot be done unless you have kept a record of the game.
Correspondence and e-mail chess are not possible without chess notation. For that matter, chess played over the telephone and blindfold chess are also prohibitively difficult without a notation system.
There have been more books written about chess than about all other games combined. The game has a wide appeal, and its language is understood all over the world. Knowing the language of chess can put you in touch with people from every corner of the globe.