The “Quick Saves” is basically a folder in the Save menu which can be accessed quickly by clicking on the button. It only has 8 slots instead of regular saving (which can have infinite number of pages).

I recommend using the quick saves folder for serious playthroughs or when you feel that you arrived at a critical checkpoint in the game. On the other hand, you can use the regular saving menu for all the slightly different variations that you want to try out in the storyline!

Be careful though, Quick Saves will overwrite once you've used all 8 slots, so save wisely!