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.
Writing things down
Sort:
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.
Oct 15, 2017
0
#8
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).
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)