Recording your chess moves is important! It's required in every tournament except the lowest elementary levels! At first thought it might appear a tedious process, but the reality is it only takes a second and it's very easy to learn chess notation.
Why record your chess moves? It solves disputes. Say your opponent claims that you cheated or that the position isn't correct. Yeah, fortunately this is very rare... maybe since you both know the scoresheet proves the chess position!
It's also a good idea to record the chess moves on a scoresheet or inside your own scorebook. You can compile a record of your chess tournament games just like the great chess players of today and the past. How else do you think we'd be able to review those brilliancies?
Record your games in a score pad. Or if you really play serious chess, a scorebook. You'll be able to review those games any time with your chess coach or teacher, or with a friend. This way, the scorebook will help you learn from your games by enabling you to review your games and learn from mistakes which you can spot later!