The pink scenes happen when Aura has 0 effective willpower when prompted to accept/decline the scene. So it starts from her nominal willpower as seen in the status screen, and then applies other modifiers, mainly any sensitivities and fetishes that apply to the scene (e.g. Hermann scenes have Cheating) and any applicable Perversions (e.g. But It's So Cute! in any scene where Aura changes clothes).
As for what pink scenes do, other than change the text, they increase (generally double) the Corruption and sensitivity / fetish gains of the scene, and also Lewdness, although each scene has an upper limit to that (e.g. first Hermann scenes won't increase Lewdness to more than 10).
Getting pink scenes takes work at first, but gets easier and easier as Aura gets lewder and has her Willpower affected by more and more curses.