Papyrus is the name given to a new script language that Bethesda created when they developed Skyrim, or to be more precise for the Creation Kit.
(Actually in-house development used different tools than the CK but for the sake of expediency, I'll just say the CK.)
Skyrim is a game that was developed to use the same basic structure as games that preceded it such as: Morrowind, Oblivion, Fallout 3 & Fallout New Vegas. These games too had scripts that accomplished tasks in-game, but it was not Papyrus. Note this last phrase!
Now when Skyrim, and now Fallout 4, was developed a lot was made of the use of Papyrus and the fact it has an entry in the configuration INI for it to log events and the success or failure of the script functions. This is where new users need to realise that Papyrus logging is not a tool to diagnose CTDs, ILSs or any other issues you might face in your game.
It's sole purpose can be told in one short sentence added to the header of every log that one of the Bethesda developers mentions here. (Thanks to @alt3n1ty for this tidbit)
(Nb. This is in FO4 logs, not Skyrim, so don't go looking for them in your Skyrim logs and come back and tell me different.)
Another point to remember. The mechanism that logs these scripts is part of the game engine and if it, the game engine, crashes it is impossible for it to log what happened because it itself is now... crashed. You will need a process running separately to the game engine to track the calls made by it and to it in the same way as software developers run bugtrackers on their software.
e.g. MO's logs can be used for some minor error tracking because MO's 'hooking' code is running separately to the game and does not CTD when the game does.
Now let's go back to the point about Skyrim being the next game in a long line of games all designed similarly. When a gamer running Morrowind, Oblivion, Fallout 3 or Fallout New Vegas had a CTD or ILS what did they use to diagnose their issues? Could they enable Papyrus logging to help them?
No, they did what all gamers did, they looked at the real issue: memory. The biggest culprit is large texture mods or other such things that tax the system to a point where it just 'throws up its hands and surrenders'. Nowhere did they consider a script logging mechanism would assist them, because one didn't exist.
These issues have existed since there were games and the means to diagnose and fix them have also existed. All before the introduction of Papyrus.
Long story short: turn off your Papyrus logging and DO NOT USE it to diagnose general game issues. Only enable it if you are assisting a modder to diagnose a script in their mod and they ask you to do so.