It’s a confirmation that they wish to perform an action that will result in the loss of information (the game state). You’ll notice that usually this only happens from in-game and rarely quitting from the main menu because the main menu has no information to lose.
The goal is to prevent players from accidentally quitting the game and losing playtime that they haven’t saved. It’s the same reason Word, or Notepad or whatever other desktop application you want to name does the same thing when you try to close the app. Now they usually have the benefit of knowing if you have unsaved changes and not prompting you. Game’s a usually too complicated or have changes happening in the background, so we’ll always prompt.
On consoles, one of the certification requirements is/was called “Confirmation of destructive action” and if the player could accidentally do anything that couldn’t be undone (and wasn’t part of a gameplay action) you had to have a confirmation or else you would/could get denied and have to certify again (which you really didn’t want to do). Things like quitting the game, deleting saves and even loading a game while already in a session.
So no, it’s not about boosting stats. But short of a joke implementation, there should only ever be one prompt to confirm the action.