Why is it important?
First, both of you have just finished the game, so you can remember it clearly. Most times you don't need your score sheet. Your ideas and thoughts are still vivid in your mind. You can exchange your ideas with your opponent, getting some critique, or learning some new perspectives. If your opponent is stronger and honest, you can learn a lot from the review. Even when your opponent is weaker, you can still learn something that you might miss when you think during the game. No one is perfect.
Second, at this moment, the competition is over. The exchange is more friendly. Sometimes you can build up new friendship during your review.
Third, the review forces you remember your moves (no one wants to be seen as the one who can't remember anything and has to copy moves from his/her score sheet). This indirectly enhances your memory.
Do NOT fear you might show your opponent too much of your secret weapon, if you have any. It's rare that you will play the same opponent again using the same moves.