Writing things down

Whenever I watch some chess matches, I notice sometimes, the players will write something on paper. Are these the moves that are being made? Just curious x)

Yes they are the moves being made.

In a tournament setting FIDE requires you write down the moves of the game, so people can analyze and review it later.

Oooh, ok. What do they try to find when analyzing it? I'm still inexperienced so sorry if it's a stupid question x)

They are trying to find how they could have played better, or were they blundered.

I see, thanks!

No problem.

There's another reason. In order to make certain claims (such as draw by threefold repetition, 50-move rule, opponent's flag fell before required number of moves made), a player must have an accurate score sheet so the TD can verify the claim.

They are not allowed to write other things than the moves. Wesley So lost a game by forfeit vs Var Akobian at the US championship a couple of years ago for writing 'inspirational notes' to himself. (He had been warned previously that it was not allowed and Akobian alerted the arbiter).